28,767 research outputs found
Notes on Interpolation in the Generalized Schur Class. II. Nudelman\u27s Problem
An indefinite generalization of Nudel′man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for Pick-Nevanlinna and Carath´eodory-Fej´er interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel′man’s problem
On the trace theorem to Volterra-type equations with local or non-local derivatives
This paper considers traces at the initial time for solutions of evolution
equations with local or non-local derivatives in vector-valued weighted
spaces. To achieve this, we begin by introducing a generalized real
interpolation method. Within the framework of generalized interpolation theory,
we make use of stochastic process theory and two-weight Hardy's inequality to
derive our trace and extension theorems. Our results encompass findings
applicable to time-fractional equations with broad temporal weight functions
On The Properties Of -Bernstein-Type Polynomials
The aim of this paper is to give a new approach to modified -Bernstein
polynomials for functions of several variables. By using these polynomials, the
recurrence formulas and some new interesting identities related to the second
Stirling numbers and generalized Bernoulli polynomials are derived. Moreover,
the generating function, interpolation function of these polynomials of several
variables and also the derivatives of these polynomials and their generating
function are given. Finally, we get new interesting identities of modified
-Bernoulli numbers and -Euler numbers applying -adic -integral
representation on and -adic fermionic -invariant integral
on , respectively, to the inverse of -Bernstein polynomials.Comment: 17 pages, some theorems added to new versio
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