Displaying similar documents to “A study of resolvent set for a class of band operators with matrix elements”

Factorization makes fast Walsh, PONS and other Hadamard-like transforms easy

Kautsky, Jaroslav

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A simple device, based on the factorization of invertible matrix polynomials, enabling to identify the possibility of fast implementation of linear transforms is presented. Its applicability is demonstrated in the case of Hadamard matrices and their generalization, Hadamard matrix polynomials.

Some relations on Humbert matrix polynomials

Ayman Shehata (2016)

Mathematica Bohemica

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The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix...

Rota-Baxter operators and Bernoulli polynomials

Vsevolod Gubarev (2021)

Communications in Mathematics

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We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.

On Erb's uncertainty principle

Hubert Klaja (2016)

Studia Mathematica

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We improve a result of Erb, concerning an uncertainty principle for orthogonal polynomials. The proof uses numerical range and a decomposition of some multiplication operators as a difference of orthogonal projections.

Polynomials in the Volterra and Ritt operators

Dashdondog Tsedenbayar, Jaroslav Zemánek (2005)

Banach Center Publications

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We continue the paper [Ts] on the boundedness of polynomials in the Volterra operator. This provides new ways of constructing power-bounded operators. It seems interesting to point out that a similar procedure applies to the operators satisfying the Ritt resolvent condition: compare Theorem 5 and Theorem 9 below.

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

Irina Karelin, Leonid Lerer (2001)

International Journal of Applied Mathematics and Computer Science

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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...

A fixed point method to compute solvents of matrix polynomials

Fernando Marcos, Edgar Pereira (2010)

Mathematica Bohemica

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Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.

Absolutely Summing Terraced Matrices

Ibrahim Almasri (2016)

Concrete Operators

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Let α > 0. By Cα we mean the terraced matrix defined by [...] if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be [...] in the region 1/p + 1/q ≤ 1.