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New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative

Part of the Operator Theory: Advances and Applications Book Series (volume 286)

Editors: Alpay, Daniel; Peretz, Ronen; Shoikhet, David; Vajiac, Mihaela B.

DOI: 10.1007/978-3-030-76473-9

ISBN: 978-3-030-76472-2

Publisher: Springer International Publishing - Springer Journals

May 21, 2021

1 - 10 of 12 Chapters

LitStream

Chapter 1On Parseval Frames of Kernel Functions in de Branges Spaces of Entire Vector Valued Functions

Al-Sa’di, Sa’ud; Weber, Eric S.

Pages: 1 –18

[We consider the existence and structure properties of Parseval frames of kernel functions in vector valued de Branges spaces. We develop some sufficient conditions for Parseval sequences by identifying the main construction with Naimark dilation of frames. The dilation occurs by embedding the de...
LitStream

Chapter 2Differential Subordinations in Harmonic Mappings

Aydogan, M.; Bshouty, D.; Miller, S. S.; Sakar, F. M.

Pages: 19 –27

[Differential subordination of analytic functions proved to be useful in many applications. The book of Miller and Mocanu ((2000) Differential Subordinations. In Theory and applications, monographs and textbooks in pure and applied mathematics, vol 225. Marcel Dekker Inc, New York) sums up most...
LitStream

Chapter 3The Segal–Bargmann Transform in Clifford Analysis

Bernstein, Swanhild; Schufmann, Sandra

Pages: 29 –52

[The Segal–Bargmann transform plays an essential role in signal processing, quantum physics, infinite-dimensional analysis, function theory and further topics. The connection to signal processing is the short-time Fourier transform, which can be used to describe the Segal–Bargmann transform. The...
LitStream

Chapter 4On the Carathéodory-Fejér Interpolation Problem for Stieltjes Functions

Bolotnikov, Vladimir

Pages: 53 –85

[The following Carathéodory-Fejér problem is considered: given a point x0 < 0 and numbers c0, c1, …, cN ≥ 0, to construct a Stieltjes-class function f such that fj(x0)∕j! = cj for j = 0, 1, …, N. The cases where N is odd or even are quite different. For each case, the solvability criterion is...
LitStream

Chapter 5Harmonic Analysis of Some Arithmetical Functions

Gay, Roger; Sebbar, Ahmed

Pages: 87 –137

[We study three functions which are power series in the variable z, Dirichlet series in the variable s and with coefficients given by arithmetical functions. A strong point is to relate these functions to some Hilbert spaces. Three main ingredients are used: an estimate of Davenport on sums of...
LitStream

Chapter 6Symmetric Measures, Continuous Networks, and Dynamics

Bezuglyi, Sergey; Jorgensen, Palle E. T.

Pages: 139 –197

[With view to applications, we here give an explicit correspondence between the following two: (i) the set of symmetric and positive measures ρ on one hand, and (ii) a certain family of generalized Markov transition measures P, with their associated Markov random walk models, on the other. By a...
LitStream

Chapter 7Multi Variable Semicircular Processes From ∗-Homomorphisms and Operators

Cho, Ilwoo; Jorgensen, Palle E. T.

Pages: 199 –242

[In this paper, we (i) consider a Banach ∗-probability space 𝕃Q(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 8Representation Formulae for the Determinant in a Neighborhood of the Identity

Constales, Denis; Guzmán Adán, Alí

Pages: 243 –257

[We prove an integral representation and a power series expansion for the function det(A)−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 9Parametrization of the Solution Set of a Matricial Truncated Hamburger Moment Problem by a Schur Type Algorithm

Fritzsche, Bernd; Kirstein, Bernd; Kley, Susanne; Mädler, Conrad

Pages: 259 –328

[This paper contains a Schur analytic approach to a truncated matricial moment problem of Hamburger type, which is studied in the most general case. It is shown that a Schur type algorithm constructed by the authors for a related moment problem can be suitably modified to obtain a full...
LitStream

Chapter 10The Wiener Algebra and Singular Integrals

Liflyand, E.

Pages: 329 –339

[Salem type conditions for trigonometric series are extended to functions from the Wiener algebra. While in the earlier one-dimensional generalization the conditions are given in terms of the Hilbert transform, for the multivariate setting all reasonable singular integrals are equally involved.]

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