Related papers: Estimates on some functionals over non-linear reso…
The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and…
This paper focuses on estimating the Taylor coefficients for Hilbert spaces of holomorphic functions on the disk using intrinsic features of univalent functions and of Teichmuller spaces. Estimating these coefficients has a long history but…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Goedel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones.…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
In this paper we establish square-function estimates on the double and single layer potentials for divergence-form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This…
For non-anticipative functionals, differentiable in Chitashvili's sense, the It\^o formula for cadlag semimartingales is proved. Relations between different notions of functional derivatives are established.
In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are…
Making use of the Hadamard product(or convolution), we find some estimates on the Taylor-Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ for functions belong to bi univalent functions of the Bazilevi$\check{c}$ type of order $\gamma$.…
This article presents the convergence analysis of a sequence of piecewise constant and piecewise linear functions obtained by the Rothe method to the solution of the first order evolution partial differential inclusion…
We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical…
We consider the Polya--Szeg\"o type weighted inequality. We prove this inequality for monotone rearrangement and for Steiner's symmetrization.
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood…
We present an algorithm producing all rational functions $f$ with prescribed $n+1$ Taylor coefficients at the origin and such that $\|f\|_\infty\le 1$ and $\deg f\le k$ for every fixed $k\ge n$. The case where $k<n$ is also discussed.
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson…
We present an overview of the existing methods for computing functional determinants, and outline a possible way forward for Hamiltonians of higher dimensions without radial symmetry.
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…