Carlson's Theorem Research Articles

Carlson's theorem for different measures

We use an observation of Bohr connecting Dirichlet series in the right half plane C+ to power series on the polydisk to interpret Carlson's theorem about integrals in the mean as a special case of the ergodic theorem by considering any vertical line in the half plane as an ergodic flow on the polytorus. Of particular interest is the imaginary axis because Carlson's theorem for Lebesgue measure does not hold there. In this note, we construct measures for which Carlson's theorem does hold on the imaginary axis for functions in the Dirichlet series analog of the disk algebra A(C+).

Application of the Euler's gamma function to a problem related to F. Carlson's uniqueness theorem

In his work on F. Carlson's uniqueness theorem for entire functions of exponential type, Q. I. Rahman [5] was led to consider an infinite integral and needed to determine the rate at which the integrand had to go to zero for the integral to converge. He had an estimate for it which he was content with, although it was not the best that could be done. In the present paper we find a result about the behaviour of the integrand at infinity, which is essentially best possible. Stirling's formula for the Euler's Gamma function plays an important role in its proof.

On formulas for π experimentally conjectured by Jauregui–Tsallis

In a recent study of representing Dirac's delta distribution using q-exponentials, Jauregui and Tsallis experimentally discovered formulae for π as hypergeometric series as well as certain integrals. Herein, we offer rigorous proofs of these identities using various methods and our primary intent is to lay down an illustration of the many technical underpinnings of such evaluations. This includes an explicit discussion of creative telescoping and Carlson's Theorem. We also generalize the Jauregui–Tsallis identities to integrals involving Chebyshev polynomials. In our pursuit, we provide an interesting tour through various topics from classical analysis to the theory of special functions.

Numerical recovery of location and residue of poles of meromorphic functions

We present a method able to recover location and residue of poles of functions meromorphic in a half--plane from samples of the function on the real positive semi-axis. The function is assumed to satisfy appropriate asymptotic conditions including, in particular, that required by Carlson's theorem. The peculiar features of the present procedure are: (i) it does not make use of the approximation of meromorphic functions by rational functions; (ii) it does not use the standard methods of regularization of ill-posed problems. The data required for the determination of the pole parameters (i.e., location and residue) are the approximate values of the meromorphic function on a finite set of equidistant points on the real positive semi-axis. We show that this method is numerically stable by proving that the algorithm is convergent as the number of data points tends to infinity and the noise on the input data goes to zero. Moreover, we can also evaluate the degree of approximation of the estimates of pole location and residue which we obtain from the knowledge of a finite number of noisy samples.

Note on Carlson's Theorem

Note on Carlson's Theorem

The classification of torsion endo-trivial modules

The main purpose of this paper is to show that, if G is a finite p-group which is not cyclic, quaternion or semi-dihedral, then the group of endo-trivial G-modules is detected on restriction to elementary abelian p-subgroups of rank 2. Consequently, the torsion subgroup of the group of endo-trivial modules is trivial for any finite p-group, except in the known cases of cyclic, quaternion and semi-dihedral groups. This requires a large amount of group cohomology, recent bounds for the number of Bocksteins in Serre's theorem, Carlson's recent theorem expressing Serre's theorem in terms of modules, and finally the theory of varieties attached to modules. A detection theorem for the torsion subgroup of the Dade group of all endo-permutation modules is deduced from the main theorem. The structure of this torsion subgroup can then be fully described when p is odd (using the results of Bouc-Thevenaz).

Variations on the theme of the Carlson theorem

Variations on the theme of the Carlson theorem

An extension of Carlson's theorem for entire functions of exponential type

An extension of Carlson's theorem for entire functions of exponential type

Carlson's theorem on varieties and transfer

J. Carlson has proved for finite groups that the variety in spec H ev( BG, F p ) defined by the ideal generated by the images of transfers from all subgroups of index divisible by p is the same as the variety defined by the kernel of the restriction to the center of a p-Sylow subgroup. We prove a generalization of this theorem for compact Lie groups. For finite groups the proof specializes to a purely algebraic proof which is a bit shorter and somewhat more direct than Carlson's original proof.

Carlson's theorem for harmonic functions

Soit f(z) une fonction entiere de type exponentiel inferieur a π avec {f(m+i)∈l 1 . Si f(m)=0, ∞<m<∞, alors f/z)≡0

Lerch's theorem for analytic functional with non-compact carrier and its applications to entire functions

A Lerch's theorem for analytic functionals with unbounded carrier is proved. As applications Carlson's theorem, Polya's theorem and a Phragmen-Lindelof type theorem are obtained for entire functions of exponential type in the left halfplane and of type 1 with respect to proximate order 1 + (log logr)/(logr) in the right half plane.

An extension of Carlson's theorem for entire functions of exponential type, II

An extension of Carlson's theorem for entire functions of exponential type, II

An Extension of Carlson's Theorem for Entire Functions of Exponential Type

An Extension of Carlson's Theorem for Entire Functions of Exponential Type

Carlson theorem for harmonic functions in Rn

Carlson theorem for harmonic functions in Rn

Shorter Notes: Necessary and Sufficient Conditions for Carlson's Theorem for Entire Functions

Shorter Notes: Necessary and Sufficient Conditions for Carlson's Theorem for Entire Functions

Renormalization and Ward identities using complex space-time dimension

Complex-dimensional renormalization is defined for an arbitrary Feynman amplitude and shown to be equivalent to BPH renormalization. Using quantum electrodynamics as an example, Ward identities are proved; here Carlson's theorem extends the identities from integer to complex dimension. Both complex dimensional and analytic regularization are necessary at intermediate stages.

O(4)Expansion of the Bethe-Salpeter Equation forπρScattering

In the context of the Bethe-Salpeter equation, we study the properties of the $O(4)$ expansion of the $\ensuremath{\pi}\ensuremath{\rho}$ scattering amplitude. We find that the expansion has the required kinematical singularities. Assuming that the Regge trajectory of the pion has $M=1$ at $t=0$, we examine the form of the $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rho}$ vertex functions for two trajectory-mixing models. We also show that our expansion satisfies Carlson's theorem.

Necessary and Sufficient Conditions for Carlson's Theorem on Entire Functions

Necessary and Sufficient Conditions for Carlson's Theorem on Entire Functions

On Carlson's theorem in the theory of the zeta-function of Riemann

On Carlson's theorem in the theory of the zeta-function of Riemann

A Generalization of Carlson's Theorem

Journal of the London Mathematical SocietyVolume s1-21, Issue 2 p. 106-110 Notes and papers A Generalization of Carlson's Theorem W. H. J. Fuchs, W. H. J. Fuchs University College, SwanseaSearch for more papers by this author W. H. J. Fuchs, W. H. J. Fuchs University College, SwanseaSearch for more papers by this author First published: April 1946 https://doi.org/10.1112/jlms/s1-21.2.106Citations: 20AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volumes1-21, Issue2April 1946Pages 106-110 RelatedInformation