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18,662
result(s) for
"analytic functions"
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Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and
operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the
Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and
then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a
certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér
Interpolation Problem for matrix rational functions. We then extend the
eBook
On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function
We present several formulae for the large
eBook
Embeddings of Decomposition Spaces
Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an
embedding between the two?
A decomposition space
We establish readily verifiable criteria which ensure the
existence of a continuous inclusion (“an embedding”)
In a nutshell, in order to apply the embedding results presented in this
article, no knowledge of Fourier analysis is required; instead, one only has to study the geometric properties of the involved
coverings, so that one can decide the finiteness of certain sequence space norms defined in terms of the coverings.
These
sufficient criteria are quite sharp: For almost arbitrary coverings and certain ranges of
We also prove a
The resulting embedding theory is illustrated by applications
to
eBook
Recent progress on operator theory and approximation in spaces of analytic functions : Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, June 29-July 3, 2015, Institut Mittag-Leffler, Djursholm, Sweden
This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29-July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden.The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures.This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.
eBook
On Third-Order Differential Subordination Results for Univalent Analytic Functions Involving An Operator
In this paper, by making use An operator, suitable classes of admissible functions are investigated and the properties of third-order differential subordination are obtained.
Journal Article
Approximation of analytic functions by generalized shifts of the Lerch zeta-function
In the paper, we approximate analytic functions by generalized shifts of the Lerch zeta-function, where g is a certain increasing to real function having a monotonic derivative. We prove that, for arbitrary parameters λ and α, there exists a closed set of analytic functions defined in the strip 1/2 < σ < 1 which functions are approximated by the above shifts. If the set of logarithms is linearly independent over the field of rational numbers, then the set coincides with the set of all analytic functions in that strip.
Journal Article
Descriptions of Spectra of Algebras of Bounded-Type Block-Symmetric Analytic Functions
This paper is devoted to the study of the algebra of bounded-type block-symmetric analytic functions on the Banach space l1(Cs). In particular, it presents a description of the spectrum of this algebra in terms of exceptional characters ϕα and characters that can be associated with exponential-type functions of several variables with plane zeros. Due to this representation, it is proven that every element of the spectrum is a convolution of an exceptional character with a point evaluation functional.
Journal Article
Numerical analytic continuation
Let
f
be an analytic function on a simply-connected compact continuum
E
of the complex
z
-plane. This might be an interval of the real line, where
f
might be real analytic. How can we calculate good estimates of the analytic continuation of
f
to other points
z
∈
C
? How can we estimate the locations of real or complex singularities of
f
? We review both the theory and the practice of some existing methods for these problems and propose that excellent results can be obtained from the computation of rational approximations of
f
by the AAA algorithm. In the case of analytic functions of two or more variables, the rational approximations are applied along line segments or other analytic arcs.
Journal Article
Block-Supersymmetric Polynomials on Spaces of Absolutely Convergent Series
In this paper, we consider a supersymmetric version of block-symmetric polynomials on a Banach space of two-sided absolutely summing series of vectors in Cs for some positive integer s>1. We describe some sequences of generators of the algebra of block-supersymmetric polynomials and algebraic relations between the generators for the finite-dimensional case and construct algebraic bases of block-supersymmetric polynomials in the infinite-dimensional case. Furthermore, we propose some consequences for algebras of block-supersymmetric analytic functions of bounded type and their spectra. Finally, we consider some special derivatives in algebras of block-symmetric and block-supersymmetric analytic functions and find related Appell-type sequences of polynomials.
Journal Article