Generalized Fock spaces, interpolation, multipliers, circle geometry.

Título inglés Generalized Fock spaces, interpolation, multipliers, circle geometry.
Título español Espacios de Fock generalizados, interpolación, multiplicadores, geometría del círculo.
Autor/es Peetre, Jaak ; Thangavelu, Sundaram ; Wallin, Nils-Olof
Organización Mat. Inst. Lunds Univ., Lund, Suecia;Stat-Math Div. Indian Stastist. Inst., Bangalore, India
Revista 0213-2230
Publicación 1996, 12 (1): 63-110, 17 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e-Q(z), where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle C in C. We consider the problem of interpolation between two Fock spaces. If C0 and C1 are the corresponding circles, one is led to consider the pencil of circles generated by C0 and C1. If H is the one parameter Lie group of Moebius transformations leaving invariant the circles in the pencil, we consider its complexification Hc, which permutes these circles and with the aid of which we can construct the Calderón curve giving the complex interpolation. Similarly, real interpolation leads to a multiplier problem for the transformation that diagonalizes all the operators in Hc. It turns out that the result is rather sensitive to the nature of the pencil, and we obtain nearly complete results for elliptic and parabolic pencils only.
Clasificación UNESCO 120214
Palabras clave español Interpolación ; Operadores de Fock ; Espacios de Fock ; Espacios de Hilbert
Código MathReviews MR1387587
Código Z-Math Zbl 0849.46015
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