### ?

## Systems of reproducing kernels and their biorthogonal: completeness or incompleteness?

International Mathematics Research Notices. 2011. No. 22. P. 5076–5108.

Baranov A., Belov Y.

Language:
English

Remizov I., Infinite Dimensional Analysis, Quantum Probability and Related Topics 2018 Vol. 21 No. 4 P. 1850025-1–1850025-35

A parabolic partial differential equation u 0 t (t, x) = Lu(t, x) is considered, where L is a linear second-order differential operator with time-independent (but dependent on x) coefficients. We assume that the spatial coordinate x belongs to a finite- or infinitedimensional real separable Hilbert space H. The aim of the paper is to ...

Added: October 5, 2018

Eichberger J. T., Pirner H. J., Journal of Mathematical Economics 2018 Vol. 78 No. C P. 131–141

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox to illustrate the potential ...

Added: May 19, 2020

Ulyanov V. V., Prokhorov Y., , in : Springer Proceedings in Mathematics and Statistics. Vol. 42: Limit Theorems in Probability, Statistics and Number Theory, In Honor of Friedrich Götze.: Berlin: Springer, 2013. P. 235–249.

We review the results about the accuracy of approximations for distributions of functionals of sums of independent random elements with values in a Hilbert space. Mainly we consider recent results for quadratic and almost quadratic forms motivated by asymptotic problems in mathematical statistics. Some of the results are optimal and could not be further improved ...

Added: May 1, 2014

Martynov G., , in : Festschrift in honor of Paul Deheuvels. : Springer, 2014.

In statistical applications it is often assumed that an observed random process is Gaussian. We propose a statistical method for testing the null hypothesis that an observed random process on the interval $[0,1]$ is a mean zero Gaussian process with specified covariance function. Our method is based on a finite number of observations of the ...

Added: March 23, 2014

Remizov I., Modeling and Analysis of Information Systems 2015 Vol. 22 No. 3 P. 337–355

A parabolic partial differential equation 𝑢′𝑡(𝑡, 𝑥) = 𝐿𝑢(𝑡, 𝑥) is considered, where 𝐿 is a linear second-order differential operator with time-independent coefficients, which may depend on 𝑥. We assume that the spatial coordinate 𝑥 belongs to a finite- or infinite-dimensional real separable Hilbert space 𝐻. Assuming the existence of a strongly continuous resolving semigroup ...

Added: October 30, 2018

Protasov V., Широков М. Е., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2019 Т. 489 № 5

Рассматриваются два преобразования функций на полупрямой и доказывается,что их композиция дает вогнутую мажоранту для любой неотрицательной функции.В частности, на классе неотрицательных вогнутых функций данная композиция есть тождественное преобразование. Указаны приложения этого результата в теории операторов в гильбертовом пространстве и в теории квантовых систем. Сформулирован ряд открытых задач. ...

Added: October 31, 2019

Veretennikov A., Da Prato G., Flandoli F. et al., / Cornell University. Series cond-mat "arxiv.org". 2014. No. arXiv:1404.5418.

We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose non-linear drift parts are sums of the subdifferential of a convex function and a bounded part. This generalizes a classical result by one of the authors (Veretennikov) to infinite dimensions. ...

Added: October 22, 2014

Galkin S., Belmans P., Mukhopadhyay S., / Cornell University. Series math "arxiv.org". 2020. No. 2009.05568.

We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode degenerations of the moduli space of rank 2 bundles with fixed determinant. We show that the birational type of the graph potential only depends on the homotopy type of ...

Added: April 15, 2021

Protasov V., Shirokov M., Doklady Mathematics 2019 Vol. 100 No. 3 P. 1–4

Two transforms of functions on a half-line are considered. It is proved that their composition gives a concave majorant for every non-negative function. In particular, this composition is an identical transform on the class of non-negative functions. Applications of this result in the operator theory of Hilbert space and in the theory of quantum systems are mentioned. ...

Added: December 5, 2019