Local semigroups of isometries in \(\Pi_ \kappa\)-spaces and related continuation problems for \(\kappa\)-indefinite Toeplitz kernels

DOI10.1007/BF01195778zbMath0778.47024OpenAlexW2047697178MaRDI QIDQ1198108

Ramón Bruzual, Stefania A. M. Marcantognini

Publication date: 16 January 1993

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01195778

zbMATH Keywords

indefinite kernelHermitian kernelToeplitz kernelKrein-Langer theoremPontryagin space with same indexstrongly continuous local semigroup of isometries

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Groups and semigroups of linear operators (47D03) Dilations, extensions, compressions of linear operators (47A20) Positive definite functions in one variable harmonic analysis (42A82) Linear operators on spaces with an indefinite metric (47B50)

Related Items (5)

Representation of measurable positive definite generalized Toeplitz kernels in \(\mathbb{R}\) ⋮ On extensions of indefinite functions defined on a rectangle ⋮ Hermitian indefinite functions and Pontryagin spaces of entire functions. ⋮ On the local operator commutation relations and extensions of locally defined positive definite functions on the Heisenberg group ⋮ The Kreĭn-Langer problem for Hilbert space operator valued functions on the band

Cites Work

• Local semigroups of contractions and some applications to Fourier representation theorems
• Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume \(\Pi_k\). zusammenhängen. II. Verallgemeinerte Resolventen, u-Resolventen und ganze Operatoren
• Über indexerhaltende Erweiterungen eines hermiteschen Operators im Pontrjaginraum
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
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