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Algebras of Toeplitz operators with oscillating symbols.

Albrecht Böttcher, Sergei M. Grudsky, Enrique Ramírez de Arellano (2004)

Revista Matemática Iberoamericana

This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

Luchko, Yury (2008)

Fractional Calculus and Applied Analysis

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters ...

An analogue of Montel’s theorem for some classes of rational functions

R. K. Kovacheva, Julian Lawrynowicz (2002)

Czechoslovak Mathematical Journal

For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best L p -approximation with an unbounded number of finite poles are considered.

An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid

Martin Sikora (2010)

Archivum Mathematicum

The Dirac equation for spinor-valued fields f on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet H + of the hyperboloid. In particular, we derive an integral formula expressing the value of f in a chosen point p as an integral over a compact cycle given by the intersection of the null cone with H + in the Minkowski space 𝕄 .

An observation on the Turán-Nazarov inequality

Omer Friedland, Yosef Yomdin (2013)

Studia Mathematica

The main observation of this note is that the Lebesgue measure μ in the Turán-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant ω ≥ μ, which can be effectively estimated in terms of the metric entropy of a set, and may be nonzero for discrete and even finite sets. While the frequencies (the imaginary parts of the exponents) do not enter the original Turán-Nazarov inequality, they necessarily enter the definition of ω.

Analytic interpolation and the degree constraint

Tryphon Georgiou (2001)

International Journal of Applied Mathematics and Computer Science

Analytic interpolation problems arise quite naturally in a variety of engineering applications. This is due to the fact that analyticity of a (transfer) function relates to the stability of a corresponding dynamical system, while positive realness and contractiveness relate to passivity. On the other hand, the degree of an interpolant relates to the dimension of the pertinent system, and this motivates our interest in constraining the degree of interpolants. The purpose of the present paper is to...

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