Van Neerven Research Articles

Spectral Theory in Banach Spaces and Harmonic Analysis

The conference was motivated by the recent solutions of two longstanding questions. The first one is Kato's square root problem, i.e. whether for an elliptic operator in divergence form on L_2( \mathbb R^n) we have \|L^{1/2}u\|\leq C \|\nabla u\| + C\|u\| for u\in W^1_2( \mathbb R^n) . After a long development over 40 years this was shown in a joint effort by P. Auscher, S. Hofmann, M. Lacey, A. McIntosh and Ph. Tchamitchian. For a new approach to this important result via Dirac operators and extensions of it, see the abstracts of A. McIntosh and S. Keith. The second problem, attributed to Brézis in the eighties, asks whether the Cauchy problem for every generator of an analytic semigroup A in an L_q(\Omega) -space with 1<q<\infty has maximal L_p -regularity, i.e. does the solution y of the Cauchy problem y'=Ay+f , y(0)=0 , satisfy \|y\|_{W^1_p( \mathbb R_+,L_q)} \leq C \|f\|_{L_p( \mathbb R_+,L_q)} . Recently G. Lancien and N .J. Kalton gave counterexamples to this questions while L. Weis gave a characterization of maximal L_p -regularity in terms of R-boundedness. This criterium has since been shown to be useful in establishing maximal regularity for large classes of Cauchy problems for elliptic differential operators with rather general coefficients and boundary values, e.g. Schrödinger operators with singular potentials and Stokes operators (see the abstracts of M. Hieber, P. Kunstmann, J. Prüss and R. Schnaubelt). Applications of maximal regularity to non-linear differential equations were presented in the talks of H. Amann and G. Simonett. The two problems of Kato and Brézis share a common background in the mathematical methods employed in their solution, e.g. the H^\infty -functional calculus for sectorial operators in Banach spaces, boundedness of singular integral operators and square function estimates. Obviously, further progress will depend on an indepth study of these methods and their interrelations. The workshop contributions featured some of the most recent progress in these directions. N.J. Kalton used deep results from Banach space theory to crystallize the difficult perturbation theory of the H^\infty -functional calculus. Some of the randomization techniques he used can be seen as an extension of the classical square function estimates from L_p -spaces to general Banach spaces. This method also underlies boundedness results for Fourier multiplier operators, Calderón–Zygmund operators and wavelet transforms for functions with values in a Banach space with the UMD-property (see the abstracts of W. Arendt, O. Blasco, T. Hytonen and C. Kaiser) and applications of those to spectral theory (A. Gillespie). Also in the scalar-valued case several extensions of basic methods in the theory of singular integral operators were presented, e.g. new spaces of BMO- and H^1 -type associated to a given operator (X. Duong), Calderón-Zygmund operators associated to non-doubling measures (J. Garcia-Cuerva), bilinear pseudo-differential operators (A. Nahmod) and optimal domains for convolution operators (W. Ricker). As so often, new tools in harmonic analysis lead to new results for the H^\infty -functional calculus of partial differential operators (M. Cowling, X. Duong). Some of the talks reached beyond the circle of questions raised by the problems of Kato and Brézis. They were closely connected to the main topics by a shared methological background in spectral theory and harmonic analysis. Ch. Thiele discussed an approach to non-linear differential equations via the non-linear Fourier transform. B. Jefferies and J. van Neerven described the connection between spectral theory, square function estimates and stochastic integration on infinite dimensional Banach spaces. S. Grivaux and Y. Latushkin gave applications of spectral theory to instability and stability theorems for evolutionary systems. The talks of of J. Eschmeier, M. Haase and F. Sukochev were focused on the functional calculus and its applications in operator theory. The varied background of the participants lead to a number of new collaborations started during the workshop. Last but not least, the unique setting of Oberwolfach and a week of beautiful sunshine contributed to a memorable and successful meeting.

IgE-Dependent Activation of T cells by Allergen in Atopic Dermatitis: Pathophysiologic Relevance

The importance of interactions between allergen and IgE in allergen-mediated activation of T lymphocytes from patients with atopic dermatitis (AD) is unclear. A role for this interaction is implied by past evidence for IgE-facilitated presentation of allergen to T cells, but this phenomenon has only been demonstrated in specific in vitro systems biased to maximize the effect. It is therefore not known whether the process is relevant in patients. We now show that the responses to allergen of unmodified peripheral blood mononuclear cells (PBMC) from individual AD patients are significantly greater in the presence of fresh, unheated, IgE-containing autologous serum than the same serum heated under IgE-denaturing conditions or specifically depleted of IgE by immunoprecipitation. In six independent experiments, 59%-67% of the maximal in vitro PBMC response to allergen was found to be dependent upon the presence of IgE in autologous serum used at 5% final concentration. These data provide the first evidence that sufficient amounts of allergen-specific IgE and allergen-reactive T cells occur concomitantly in the blood of individual AD patients to allow IgE-enhanced T cell responses to allergen. We conclude that IgE-enhanced T cell responses are pathophysiologically relevant and a therapeutic target in AD.

Closed Semistable Operators and Singular Differential Equations

We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which 0 is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of C0-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.

Estimating the effect of NNLO contributions on global parton analyses

We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function $F_L$ and the cross sections $\sigma_W, \sigma_Z$ for $W$ and $Z$ hadroproduction as examples. For $F_L$ we find relatively poor convergence, with increasing order, at small $x$; whereas $\sigma_{W,Z}$ are much more reliably predicted.

Deep-inelastic structure functions at two loops

We present the analytic calculation of the Mellin moments of the structure functions F 2, F 3 and F L in perturbative QCD up to second-order corrections and in leading twist approximation. We calculate the two-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the two-loop coefficient functions of F 2, F 3 and F L . We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven.

Convergence of Laplace integrals

Abstract We show that the abscissa of convergence of the Laplace transform of an exponentially bounded function does not exceed its abscissa of boundedness. For C0-semigroups of operators, this result was first proved by L. Weis and V. Wrobel. Our proof for functions follows a method used by J. van Neerven in the semigroup case. P.H. Bloch gave an example of an integrable function for which the result does not hold.

Asymptotically Almost Periodic Solutions of Inhomogeneous Cauchy Problems on The Half-Line

Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t)+Au(t)+φ(t)(t⩾0). Suppose that u has uniformly convergent means, σ(A)∩iR is countable, and φ is asymptotically almost periodic. Then u is asymptotically almost periodic. Related results have been obtained by Ruess and Vũ, and by Basit, using different methods. A direct proof is given of a Tauberian theorem of Batty, van Neerven and Räbiger, and applications to Volterra equations are discussed. 1991 Mathematics Subject Classification 34C28, 44A10, 47D03.

House-dust mite antigen on skin and sheets

Although the pathophysiological role of house-dust mite (HDM) in atopic dermatitis (AD) remains controversial, reduction of exposure to HDM in the bed and bedroom has been shown to benefit AD patients. It is 16 years since Mitchell and colleagues 1 Mitchell EB Crow J Chapman MD Jouhal SS Pope FM Platts-Mills TA Basophils in allergen-induced patch test sites in atopic dermatitis.. Lancet. 1982; i: 127-130 Summary Scopus (370) Google Scholar established that application of the HDM antigen P1 (now Der p 1) to the skin of AD patients, as a patch test, induced a local delayed-type hypersensitivity response. Such atopy patch-test reactions to aeroallergens, particularly HDM, occur even on uninvolved skin, in one-third to two-thirds of children and adults with AD, predominantly in those with high specific IgE concentrations. 2 Langeveld-Wildschut EG van Marion AM Thepen T Mudde GC Bruijnzeel PL Bruijnzeel-Koomen CA Evaluation of variables influencing the outcome of the atopy patch test.. J Allergy Clin Immunol. 1995; 96: 66-73 Summary Full Text Full Text PDF PubMed Scopus (91) Google Scholar Biopsy studies reveal HDM allergens, associated with antigen-presenting cells, in the epidermis and dermis in AD but not in normal volunteers. 3 Maeda K Yamamoto K Tanaka Y Anan S Yoshida H House dust mite (HDM) antigen in naturally occurring lesions of atopic dermatitis (AD): the relationship between HDM antigen in the skin and HDM antigen-specific IgE antibody.. J Dermatol Sci. 1992; 3: 73-77 Summary Full Text PDF PubMed Scopus (48) Google Scholar Specific IgE antibodies are thought to mediate this binding and such IgE-enhanced antigen presentation has been shown to require 100–1000-fold less antigen to induce lymphocyte proliferation. 4 van der Heijden FL van Neerven RJ Kapsenberg ML Relationship between facilitated allergen presentation and the presence of allergen-specific IgE in serum atopic patients.. Clin Exp Immunol. 1995; 99: 289-293 Crossref PubMed Google Scholar Unfortunately the Der p 1 content of allergen preparations used in atopy patch tests has not often been documented, but reactions have been reported 1 Mitchell EB Crow J Chapman MD Jouhal SS Pope FM Platts-Mills TA Basophils in allergen-induced patch test sites in atopic dermatitis.. Lancet. 1982; i: 127-130 Summary Scopus (370) Google Scholar at 12·5 ng/cm 2 Langeveld-Wildschut EG van Marion AM Thepen T Mudde GC Bruijnzeel PL Bruijnzeel-Koomen CA Evaluation of variables influencing the outcome of the atopy patch test.. J Allergy Clin Immunol. 1995; 96: 66-73 Summary Full Text Full Text PDF PubMed Scopus (91) Google Scholar . The mean Der p 1 found in young children's beds in Wellington is 4·9 ng/cm 2 Langeveld-Wildschut EG van Marion AM Thepen T Mudde GC Bruijnzeel PL Bruijnzeel-Koomen CA Evaluation of variables influencing the outcome of the atopy patch test.. J Allergy Clin Immunol. 1995; 96: 66-73 Summary Full Text Full Text PDF PubMed Scopus (91) Google Scholar (range 0·01–281·2 ng/cm 2 Langeveld-Wildschut EG van Marion AM Thepen T Mudde GC Bruijnzeel PL Bruijnzeel-Koomen CA Evaluation of variables influencing the outcome of the atopy patch test.. J Allergy Clin Immunol. 1995; 96: 66-73 Summary Full Text Full Text PDF PubMed Scopus (91) Google Scholar ) of mattress surface (unpublished data). We questioned whether there might be sufficient Der p 1 on the skin surface to potentially continue to stimulate a hypersensitivity response after rising from bed.

T-cell responses to allergens: epitope-specificity and clinical relevance.

Allergen-specific T cells play an important role in the pathophysiology of atopic allergies. Recently, cDNAs that encode many important allergens have been cloned and their amino acid sequences deduced, thus allowing the elucidation of the epitope-specificity of allergen-specific T cells. Here, Joost van Neerven and colleagues discuss the results of these studies, and the implications for the development of efficient strategies for specific immunotherapy.

Rederivation of the spin-dependent next-to-leading order splitting functions.

We perform a new calculation of the polarized next-to-leading order splitting functions, using the method developed by Curci, Furmanski and Petronzio. We confirm the results of the recent calculation by Mertig and van Neerven.

Polarized double photon production in QCD to order alpha s.

We present a complete order $\alpha_s$ analysis of the process $p p\to \gamma \gamma + X$ with polarized initial states, previously studied by us with leading order structure functions. We include in our calculation new sets of parton densities evolved in NLO QCD, such as those of Gehrmann and Stirling and of Gl\"{u}ck et al., which incorporate the new anomalous dimensions of Mertig and Van Neerven in the evolution equation. A detailed phenomenological analysis is also given which includes the photon isolation. Our results indicate that the asymmetries, although not very large, should be substantial enough at RHIC energies to be measurable in future planned experiments.

Leptoproduction of heavy quarks in the fixed and variable flavor schemes.

We compare the results of the fixed-flavor scheme calculation of Laenen, Riemersma, Smith and van Neerven with the variable-flavor scheme calculation of Aivazis, Collins, Olness and Tung for the case of neutral-current (photon-mediated) heavy-flavor (charm and bottom) production. Specifically, we examine the features of both calculations throughout phase space and compare the structure function $F_2(x,Q^2)$. We also analyze the dependence of $F_2$ on the mass factorization scale $\mu$. We find that the former is most applicable near threshold, while the latter works well for asymptotic $Q^2$. The validity of each calculation in the intermediate region is dependent upon the $x$ and $Q^2$ values chosen.

Renormalization of composite operators in Yang-Mills theories using a general covariant gauge.

Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have `alien' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infra-red singularities that appear when gluonic matrix elements are taken on-shell at zero momentum transfer. Keywords: twist-two covariant gluon operator, finite part, mixing, non-abelian, anomalous dimension, Ward identity, BRST, modified LSZ reduction, Dixon, Taylor, Joglekar, Lee.

Dimensionally-regulated pentagon integrals

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2∈ dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O(∈) corrections, a result which is the dimensionally-regulated version of a D = 4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O(∈ 0).

Dispersion relations for vacuum-polarization functions in electroweak physics

We propose a class of once-subtracted dispersion relations for the vacuum-polarization functions of massive fermions, in which the subtraction constants are determined explicitly from Ward identities. We show that in perturbation theory to O(α) and O( αα s ) this approach, the alternative dispersion relations proposed by Chang, Gaemers and van Neerven, and dimensional regularization all give the same contributions to electroweak observables such as Δϱ and Δr. The threshold behaviours of the subtraction integrands are, however, very different and the two dispersion methods are expected to lead to significantly variant estimates of contributionsarising from non-perturbative tt threshold effects.

Oculomotor Control and Cognitive Processes: Normal and Pathological Aspects

Neural networks applied to the oculomotor system (D.A. Robinson). Eye movements in neurological diagnosis: Huntington's disease and congenital nystagmus (D.S. Zee). Neurophysiology of Eye Movements. Localization of targets in humans: the role of ocular muscle proprioception (D. Nommay et al). Effects of severance of the vestibular commissural pathway on the neural integrator of the oculomotor system in cat (E. Godaux, G. Cheron). Representation of three-dimensional eye movements in the cerebellar flocculus of the rabbit (J. van der Steen et al). Effects of floccular injections of noradrenergic agonists and antagonists on adaptive changes in the VOR gain (J. van Neerven et al). The Control of Eye Movements. Human vestibuloocular reflex (VOR) and vestibular velocity storage as influenced by optokinetic stimuli (E. Koenig et al). Vertical gaze stability in cat: otolithic contribution (V.E. Pettorossi et al). Post-rotational nystagmus suppression by the presentation of a single visual target in cat and man (G. Magenes et al). Adaptive mechanisms in the monkey saccadic system (P. Inchingolo et al). Human express saccades: catch trails influence the probability of their occurrence (M. Juttner, W. Wolf). Eye-Head Coordination. Adaptation of eye and head movements to reduced peripheral vision (G.M. Gauthier et al). Coupled and dissociated modes of eye-head coordination in humans to flashed visual target (S. Ron, A. Berthoz). Superior colliculus and feedback control of gaze shift in the head-free cat (D. Pelisson et al). Strategies of eye-head coordination (R. Schmid, D. Zambarbieri). Eye Movements in Pathology. Sensory and motor aspects of congenital nystagmus (R.V. Abadi et al). Head-shaking nystagmus - A clinical tool to detect peripheral and central vestibular asymmetries (M. Fetter et al). Saccadic and smooth pursuit eye movements in olivo-ponto-cerebellar atrophies (M. Spanio et al). Slow eye movement abnormalities in Wallenberg's lateral medullary syndrome (W. Waespe). Eye tracking dysfunctions in schizophrenic patients - Why is there no neuroleptic side-effect? (N. Hock et al). Eye Movements and Cognitive Processes. A mathematical analysis of the convenient viewing position hypothesis and its components (M. Brysbaert, G. d'Ydewalle). Is there an optimal landing position in words during reading of texts? (F. Vitu, J.K. O'Regan). Processing of prepositions as reflected by gaze durations (A. Wilbertz et al). The latency of saccadic eye movements to texture-defined stimuli (H. Deubel, H. Frank). Does thinking aloud influence the structure of cognitive processes? (U. Lass et al). Eye movements in visual search: a test of the limited cognitive effort hypothesis and an analysis of the search operating characteristic (A.M. Jacobs). Applied Research. Colour, effective contrast and search performance (J.L. Barbur et al). Video-oculography - An alternative method for measurement of three-dimensional eye movements (A.H. Clarke et al).

All-order summation and two-loop results for the Drell-Yan cross section

We compare the hard part of the Drell-Yan cross section calculated at two loops by Matsuura, van der Marck and van Neerven with the predictions obtained by using resummation techniques. We observe that the convergence of the resummed expression is very good for leading and next-to-leading logarithms, and we suggest that there is room for improvement in the understanding of the remaining singular terms. Nonetheless, we find that the resummed expression predicts the two-loop K-factor with impressive accuracy.

Remarks on optimized predictions for the Drell-Yan process

We discuss the optimization of the Drell-Yan pair production cross section calculated atO(αs) and compare it with theO(αs2) results of van Neerven et al. It is shown that the optimized predictions do agree analytically with the latter calculation near the phase space boundary. They also provide a good numerical approximation wherever the stability equations have a solution.

Soft-gluon corrections to short-distance hadronic cross sections

Soft-gluon corrections which occur when hadronic cross sections are normalized by deeply inelastic scattering structure are organized to all orders. They are shown to exponentiate in terms of moments, including non-leading logarithms. The result of van Neerven's explicit calculation of the α 2 s ln 3 (n) term for Drell-Yan is rederived from one-loop calculations.