The Gohberg Anniversary Collection: Volume II: Topics in Analysis and Operator Theory: 41 (Operator Theory: Advances and Applications) - Tapa dura

 
9783764323080: The Gohberg Anniversary Collection: Volume II: Topics in Analysis and Operator Theory: 41 (Operator Theory: Advances and Applications)
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ISBN 10: 3764323086 ISBN 13: 9783764323080
Editorial: Birkhäuser, 1989

Sinopsis

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges’ characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall also make some connections with the notation of displacement rank which has been introduced and extensively studied by Kailath and a number of his colleagues as well as the one used by Heinig and Rost [HR). The first of the two classes of spaces alluded to above is distinguished by a reproducing kernel of the special form K (>.) = J - U(>’)JU(w)* (Ll) w Pw(>’) , in which J is a constant m x m signature matrix and U is an m x m J inner matrix valued function over ~+, where ~+ is equal to either the open unit disc ID or the open upper half plane (1)+ and Pw(>’) is defined in the table below.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges' characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall also make some connections with the notation of displacement rank which has been introduced and extensively studied by Kailath and a number of his colleagues as well as the one used by Heinig and Rost [HR). The first of the two classes of spaces alluded to above is distinguished by a reproducing kernel of the special form K (>.) = J - U(>')JU(w)* (Ll) w Pw(>') , in which J is a constant m x m signature matrix and U is an m x m J inner matrix valued function over ~+, where ~+ is equal to either the open unit disc ID or the open upper half plane (1)+ and Pw(>') is defined in the table below.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
1989
Idioma
Inglés
ISBN 10 
3764323086
ISBN 13 
9783764323080
Encuadernación
Tapa dura
Número de páginas
560
Editor
Kaashoek Marinus, Lancaster Peter, Goldberg Seymour
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9783034899758: The Gohberg Anniversary Collection: Volume II: Topics in Analysis and Operator Theory: 41 (Operator Theory: Advances and Applications)

Edición Destacada

ISBN 10:  3034899750 ISBN 13:  9783034899758
Editorial: Birkhäuser, 2011
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