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Factorization of rational matrix functions and difference equations

J.S. Rodríguez, L.F. Campos (2013)

Concrete Operators

In the beginning of the twentieth century, Plemelj introduced the notion of factorization of matrix functions. The matrix factorization finds applications in many fields such as in the diffraction theory, in the theory of differential equations and in the theory of singular integral operators. However, the explicit formulas for the factors of the factorization are known only in a few classes of matrices. In the present paper we consider a new approach to obtain the factorization of a rational matrix...

Failure of weak holomorphic averaging on multiple connected domains.

Jeffrey Diller (1994)

Mathematische Zeitschrift

Fejér–Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle

Jeffrey S. Geronimo, Plamen Iliev (2014)

Journal of the European Mathematical Society

We give a complete characterization of the positive trigonometric polynomials $Q (θ, ϕ)$ on the bi-circle, which can be factored as $Q (θ, ϕ) = | p (e^{i θ}, e^{i ϕ}) |^{2}$ where $p (z, w)$ is a polynomial nonzero for $| z | = 1$ and $| w | \leq 1$ . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight $\frac{1}{4 π^{2} Q (θ, ϕ)}$ on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities relating...

Finite-infinite-range inequalities in the complex plane.

Mhaskar, H.N. (1991)

International Journal of Mathematics and Mathematical Sciences

Finitely valent locally biholomorphic mappings of multiconnected domains onto the plane.

Graf, S.Yu., Starkov, V.V. (2009)

Sibirskij Matematicheskij Zhurnal

Fixed points of the derivative and $k$ -th power of solutions of complex linear differential equations in the unit disc.

Zhang, Guowei, Chen, Ang (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Formes linéaires $p$ -adiques

Daniel Barsky (1969/1970)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Formules d'interpolation et théorèmes d'unicité pour des fonctions harmoniques de type exponentiel

Raphaële Supper (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Formules intégrales pour les formes différentielles de type $(p, q)$ dans les variétés de Stein

Jean-Pierre Demailly, Christine Laurent-Thiébaut (1987)

Annales scientifiques de l'École Normale Supérieure

Free interpolation in Hardy-Orlicz spaces

Andreas Hartmann (1999)

Studia Mathematica

Function Algebras and Flows. III.

Paul S. Muhly (1974)

Mathematische Zeitschrift

Fundamental solutions for Dirac-type operators

Swanhild Bernstein (1996)

Banach Center Publications

We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces $C^{1} (G)$ and $W_{p}^{1} (G)$ . Further, we consider the Cauchy problem for this operator.

Funktionalgleichungen und Randwertaufgaben

M. Čanak (1988)

Matematički Vesnik

Further convergence results for two quadrature rules for Cauchy type principal value integrals

Nikolaos I. Ioakimidis (1982)

Aplikace matematiky

New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to $\frac{1}{2}$ . The results obtained here supplement...

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