Abstract band method via factorization, positive and band extensions of multivariable almost periodic matrix functions, and spectral estimation. Memoirs of the American Mathematical Society; 762.

Rodman, Leiba; Spitkovskii, Ilya M.; Woerdeman, Hugo J.

ISBN 10: 0821829963 / ISBN 13: 9780821829967

Verlag: Providence, American Mathematical Society, 2002

Beschreibung

Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00539 9780821829967 Sprache: Englisch Gewicht in Gramm: 350.

Bestandsnummer des Verkäufers 2483057

Bibliografische Details

• Titel: Abstract band method via factorization, positive and band extensions of multivariable almost periodic matrix functions, and spectral estimation. Memoirs of the American Mathematical Society; 762.
• Verlag: Providence, American Mathematical Society
• Erscheinungsjahr: 2002
• Sprache: Englisch
• ISBN-10: 0821829963
• ISBN-13: 9780821829967
• Einband: Softcover
• Verkäuferkataloge:
  • SA MATHEMATIK

Über diesen Titel

Inhaltsangabe

New versions are developed of an abstract scheme, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results allow us to prove, among other things, that the band extension is continuous in an appropriate sense. Using the new versions of the abstract band method, we solve the positive extension problem for almost periodic matrix functions of several real variables with Fourier coefficients indexed in a given additive subgroup of the space of variables.This generality allows us to treat simultaneously many particular cases, for example the case of functions periodic in some variables and almost periodic in others. Necessary and sufficient conditions are given for the existence of positive extensions in terms of Toeplitz operators on Besikovitch spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property.A linear fractional parameterization of the set of all extensions is also provided. We interpret the obtained results (in the periodic case) in terms of existence of a multivariate autoregressive moving averages (ARMA) process with given autocorrelation coefficients, and identify its maximal prediction error. Another application concerns the solution of the positive extension problem in the context of Wiener algebra of infinite operator matrices. It includes the identification of the maximum entropy extension and a description of all positive extensions via a linear fractional formula. In the periodic case it solves a linear estimation problem for cyclostationary stochastic processes.

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.