Cover Image

Even positive-definite hyperbolically convex functions in a Hilbert space. Representations of Hilbert spaces by self-adjoint operators

UDC 517.98 The paper consists of two parts. In the first part, we establish sufficient and necessary conditions for the integral representation of even positive-definite hyperbolically convex (h.c.) functions $k(x),$ $x\in H$. These functions are continuous in the $j$-topology. The positive defini...

Full description

Saved in:

Bibliographic Details
Date:	2026
Main Authors:	Lopotko, O., Лопотко, Олег
Format:	Article
Language:	Ukrainian
Published:	Institute of Mathematics, NAS of Ukraine 2026
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/8379
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Integral representation of even positive-definite functions of two variables
by: Lopotko, O. V., et al.
Published: (2011)

Integral representation of even positive-definite functions of one variable
by: Lopotko, O. V., et al.
Published: (2010)

Singularly perturbed self-adjoint operators in scales of Hilbert spaces
by: Albeverio, S., et al.
Published: (2007)

Singularly perturbed self-adjoint operators in scales of Hilbert spaces
by: Kuzhel', S. A., et al.
Published: (2007)

Representations of the additive group of a nuclear space in terms of self-adjoint operators
by: Lopotko, O. V., et al.
Published: (1999)

Singular Perturbations of Self-Adjoint Operators Associated with Rigged Hilbert Spaces
by: Bozhok, R. V., et al.
Published: (2005)

On the extension of even-positive-definite functions of one and two variables
by: Lopotko, O. V., et al.
Published: (1999)

Refinement of a Hardy–Littlewood–Pólya-type inequality for powers of self-adjoint operators in a Hilbert space
by: Bilichenko, R. O., et al.
Published: (2009)

Frames in Quaternionic Hilbert Spaces
by: K. S. Sharma, et al.
Published: (2019)

Singular locally scalar representations of quivers in Hilbert spaces and separating functions
by: Redchuk, I. K., et al.
Published: (2004)

A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere
by: Jäger, J.
Published: (2019)

Estimates of approximation of elements of Hilbert space
by: V. F. Babenko, et al.
Published: (2013)

Some conditions of holomorphism in the Hilbert spaces
by: Bondar , A. V., et al.
Published: (1991)

Limiting incorrect equations in the Hilbert space
by: Pogorui , A. A., et al.
Published: (2025)

$ℂ$-differentiability of mappings of Hilbert spaces
by: Gretskii, O. S., et al.
Published: (1995)

Separating functions, spectral theory of graphs, and locally scalar representations in Hilbert spaces
by: Redchuk, I. K., et al.
Published: (2006)

On one class of nonlinear operator equations in Hilbert spaces
by: Britov, N.A.
Published: (2000)

On interpolation approximation of differentiable operators in a Hilbert space
by: Popovicheva, T. N., et al.
Published: (2006)

Approximation of unbounded operators by bounded operators in a Hilbert space
by: Bilichenko, R. O., et al.
Published: (2009)

On Transitive Systems of Subspaces in a Hilbert Space
by: Moskaleva, Y.P., et al.
Published: (2006)

Three-Hilbert-Space Formulation of Quantum Mechanics
by: Znojil, M.
Published: (2009)

On observability of linear and bilinear systems of the Hilbert space
by: Belikov , S. A., et al.
Published: (1988)

On reduction of block matrices in a Hilbert space
by: Omel’chenko, P. V., et al.
Published: (2009)

Diffusion with irregular drift in a Hilbert space
by: Osipchuk, M. M., et al.
Published: (1995)

Operators of symmetric shift in Hilbert space of symmetric analytic functions
by: O. M. Holubchak
Published: (2015)

Perturbation Theory of Operator Equations in the FréChet and Hilbert Spaces
by: Boichuk, О. A., et al.
Published: (2015)

A representation of solutions of boundary-value problems for a Schrödinger equation on a Hilbert space
by: A. A. Pokutnyj
Published: (2014)

Solvability of integrodifferential equations with nondegenerate kernel in Hilbert spaces
by: O. A. Boichuk, et al.
Published: (2023)

Asymptotic Equivalence of Triangular Differential Equations in Hilbert Spaces
by: Dang Dinh Chau, et al.
Published: (2005)

Logarithmic derivatives of diffusion measures in a Hilbert space
by: Bondarenko, V. G., et al.
Published: (2000)

Solvability of integrodifferential equations with nondegenerate kernel in Hilbert spaces
by: Boichuk, О. A., et al.
Published: (2023)

On closeness of the sum of n subspaces of a Hilbert space
by: Feshchenko, I. S., et al.
Published: (2011)

On simple $n$-tuples of subspaces of a Hilbert space
by: Samoilenko, Yu. S., et al.
Published: (2009)

On the defect of nondenseness of continuous imbeddings in the scale of Hilbert spaces
by: Bozhok, R. V., et al.
Published: (2008)

Asymptotic Equivalence of Triangular Differential Equations in Hilbert Spaces
by: Dang, Dinh Chau, et al.
Published: (2005)

On the Berezin number of operators on the reproducing kernel of Hilbert space and related questions
by: U. Yamancı, et al.
Published: (2024)

Perturbation Theory of Operator Equations in the FrйChet and Hilbert Spaces
by: A. A. Bojchuk, et al.
Published: (2015)

Essential normality of some classes of operators in tensor products of Hilbert spaces
by: Livinskii, V. O., et al.
Published: (1994)

On the Berezin number of operators on the reproducing kernel of Hilbert space and related questions
by: Yamancı, Ulaş, et al.
Published: (2024)

Hermite–Birkhoff interpolation polynomial of minimum norm in Hilbert space
by: O. F. Kashpur
Published: (2021)