On the spectral characterization of entire operators with deficiency indices \((1,1)\)

DOI10.1016/j.jmaa.2010.01.050zbMath1198.47052arXiv0909.0987OpenAlexW2963399155MaRDI QIDQ968824

Julio H. Toloza, Luis O. Silva

Publication date: 10 May 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.0987

zbMATH Keywords

spectral analysissymmetric operatorsdeficiency indicesde Branges spacesentire operators

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items (16)

Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators ⋮ de Branges Spaces and Kreĭn’s Theory of Entire Operators ⋮ Applications of de Branges Spaces of Vector-Valued Functions ⋮ Multiplication operators with deficiency indices \((p,p)\) and sampling formulas in reproducing kernel Hilbert spaces of entire vector valued functions ⋮ Cauchy-de Branges spaces, geometry of their reproducing kernels and multiplication operators ⋮ On a criterion for the determinate-indeterminate dichotomy of the moment problem ⋮ Momentum operators in two intervals: spectra and phase transition ⋮ One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum ⋮ Restrictions and extensions of semibounded operators ⋮ Directing Functionals and De Branges Space Completions in Almost Pontryagin Spaces ⋮ Extensions of symmetric operators. I: The inner characteristic function case ⋮ Point mass perturbations of spectral measures ⋮ Existence of zerofree functions \(N\)-associated to a de Branges Pontryagin space ⋮ On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions ⋮ Spectral theory of multiple intervals ⋮ Translation representations and scattering by two intervals

Cites Work

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• Existence of zerofree functions \(N\)-associated to a de Branges Pontryagin space
• Polynomials in the de Branges spaces of entire functions
• Pontryagin spaces of entire functions. I
• Space-filling curves
• M. G. Krein's lectures on entire operators
• Inverse spectral theory for one-dimensional Schrödinger operators: The \(A\) function
• De Branges spaces of entire functions closed under forming difference quotients
• Schrödinger operators and de Branges spaces.
• Hermite-Biehler functions with zeros close to the imaginary axis
• Fundamental aspects of the representation theory of Hermitian operators with deficiency index (𝑚,𝑚)
• Applications of Krein's theory of regular symmetric operators to sampling theory

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