Levinson Type Research Articles

Узагальнені обернені нерівності Єнсена-Штеффенсена та пов’язані нерівності

We compare two linear functionals that are negative on convex functions. Further, using Green's functions we give some new conditions for reversed Jensen-Steffensen and related inequalities to hold. Using Green's function we also give refinement of Levinson type generalization of reversed Jensen-Steffensen and related inequalities. The acquired results are then used for constructing mean-value theorems.

Generalizations of Levinson type inequalities via new Green functions with applications to information theory

In this paper, four new Green functions are used to generalize Levinson-type inequalities for the class of 3-convex functions. The f-divergence, Renyi entropy, Renyi divergence, Shannon entropy, and the Zipf–Mandelbrot law are also used to apply the main results to information theory.

An inverse scattering problem for eigenparameter-dependent discrete Dirac system with Levinson formula

In this paper, we have considered an inverse scattering problem for discrete Dirac operator L with eigenparameter dependent boundary condition. At the outset, the Jost solution and the Jost function of L are given. Then the zeros of the Jost function and some properties of the scattering function are examined. After finding the scattering dataset and the main equation for the operator L, the uniqueness of the kernel, continuity of the scattering function and the appropriate Levinson type formula are obtained.

Теоремы типа Левинсона и проблемы Е. М. Дынькина

Исследуются вопросы, связанные с теоремами типа Левинсона-Шeберга-Волфа в комплексном и гармоническом анализе. Обсуждаются известная проблема Е. М. Дынькина об эффективной оценке мажоранты роста аналитической функции вблизи множества особенностей и двойственная в некотором смысле проблема о скорости стремления к нулю экстремальной функции в неквазианалитическом классе Карлемана в окрестности точки, где все производные функций из этого класса обращаются в нуль. Первая проблема решена В. Мацаевым и М. Содиным. В настоящей статье получено полное решение второй проблемы Е. М. Дынькина, восходящей к Бангу. Как применение получена точная асимптотическая оценка расстояния от мнимых экспонент до алгебраических полиномов в весовом пространстве непрерывных функций на вещественной прямой. Библиография: 24 названия.

Continuity of the scattering function and Levinson type formula for Klein-Gordon s-wave equation with boundary conditon depends on spectral parameter

In this article, we consider inverse problem of scattering theory for Klein-Gordon s-wave equation with boundary condition depends on spectral parameter. We define the scattering data and we also prove that the continuity of the scattering function discussing the scattering solutions. Furthermore, we obtain Levinson type formula.

Correction to: A simple proof of a multidimensional Borg–Levinson type theorem

Correction to: A simple proof of a multidimensional Borg–Levinson type theorem

Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial

Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial

Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial

Levinson type inequalities are generalized by using Hermite interpolating polynomial for the class of mathfrak{n}-convex functions. In seek of application to information theory, some estimates for new functional are obtained based on f divergence. Inequalities involving Shannon entropies are also discussed.

Estimation of f-divergence and Shannon entropy by Levinson type inequalities via new Green\u2019s functions and Lidstone polynomial

By using new Green’s functions and Lidstone interpolating polynomial, some new generalizations of Levinson type inequalities for (2p+1)-convex functions are obtained. In seek of applications of our results to information theory, new generalizations based on f-divergence estimates are also proven. Moreover, some inequalities for Shannon entropies are deduced as well.

Levinson type inequalities for higher order convex functions via Abel\u2013Gontscharoff interpolation

In this paper, Levinson type inequalities are studied for the class of higher order convex functions by using Abel–Gontscharoff interpolation. Cebyšev, Grüss, and Ostrowski-type new bounds are also found for the functionals involving data points of two types.

Integral inequalities of Levinson's type in time scale settings

Integral inequalities of Levinson's type in time scale settings

Some inequalities of Jensen’s type for Lipschitzian maps between Banach spaces

In this article, we consider some Jensen-type inequalities for Lipschitzian maps between Banach spaces and functions defined by power series. We obtain as applications some inequalities of Levinson type for Lipschitzian maps. Applications for functions of norms in Banach spaces are provided as well.

Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique

For an arbitrary Hermitian period-$T$ Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, $S$, of the spectral parameter. We employ discrete Levinson type techniques to achieve this, which allow the analysis of the asymptotic behaviour of the solution. This enables us to construct infinitely many spectral singularities on the absolutely continuous spectrum of the periodic Jacobi operator, which are stable with respect to an $l^1$-perturbation. An analogue of the quantisation conditions from the continuous case appears, relating the frequency of the oscillation of the potential to the quasi-momentum associated with the purely periodic operator.

Levinson type inequalitis and their extensions via convexity on time scales

In this paper, we prove some new inequalities of Levinson-type on time scales. Also we will prove some new extensions of these inequalities via convexity.

Levinson\u2019s type generalization of the Jensen inequality and its converse for real Stieltjes measure

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi’s inequality. The obtained results are then applied for establishing new mean-value theorems. The results from this paper represent a generalization of several recent results.

New results about Hardy-type inequality

We give a Levinson type generalization of Hardy’s inequality with convex functions replaced by 3- convex functions at a point. Several results and examples are provided, both onedimensional and multidimensional.

An improved theory of laminated Reissner–Mindlin plates

Theories of laminated plates have been proposed that, although they lead to different plate equations, are based as ours on the assumptions that the three-dimensional deformation of each layer is of Reissner–Mindlin type and that displacement and traction vectors are continuous across layer interfaces. The distinctive feature of our present theory is that reactive stresses are associated with the internal constraints implicit in the assumed kinematics, and exploited to obtain an improved evaluation of the stress field in the three-dimensional layered body for which we propose a two-dimensional model. Application to equilibrium problems for rectangular and circular plates gives results that are in good agreement with the exact three-dimensional solutions of Levinson type we derived in a companion paper.

A discrete Levinson theorem for systems with singular limit and estimates of generalized eigenvectors of some Jacobi operators

We prove a discrete Levinson type theorem on asymptotic properties of solutions of discrete d-dimensional systems with being bounded variation sequence and with the perturbation being ‘appropriately small’, for the case when has zero eigenvalue. We use this result to obtain estimates for some generalized eigenvectors of Jacobi operators. In particular we get estimates of the eigenvectors decay for Jacobi matrices with ‘shaky weights’.

New discrete Levinson type asymptotics of solutions of linear systems

We prove new discrete versions of Levinson type theorems describing asymptotic behavior of solutions of systems of linear difference equations. We show that for several cases of equations with coefficients possessing some “essential” oscillations the asymptotics should be also essentially corrected, comparing with the classical Levinson's cases studied, e.g. in [2,5,9]. The results obtained here allow to study the asymptotics for some systems with coefficients which are not necessary convergent. As an illustration, an application to spectral studies of some Jacobi matrices is presented, by using the asymptotics of generalized eigenvectors.

Completely Indecomposable Operators and a Uniqueness Theorem of Cartwright–Levinson Type

A bounded linear operator T on a complex Hilbert space will be called completely indecomposable if its spectrum is not a singleton, and is included in the spectrum of the restrictions of T and T* to any of their nonzero invariant subspaces. Two classes of completely indecomposable operators are constructed. The first consists of essentially selfadjoint operators with spectrum [−2, 2], and the second of bilateral weighted shifts whose spectrum is the unit circle. We do not know whether any of the operators in the first class has a proper invariant subspace and if any of the operators in the second class has a proper hyperinvariant subspace. We also establish a new uniqueness theorem of Cartwright–Levinson type which is the main ingredient in our proofs of complete indecomposability.