Integral representations of unbounded operators by arbitrarily smooth Carleman kernels

2002/10/13 by Igor M. Novitskii, Novitskii, Igor M.
Mathematics · #45P05 #47G10 #Algebra over a field #Bounded function #Bounded operator #Characterization (materials science) #Computer science #FOS: Mathematics #Fourier integral operator #Functional Analysis (math.FA) #Hilbert space #Holomorphic and Operator Theory #Kernel (algebra) #Linear operators #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Operator (biology) #Operator theory #Physics #Pure mathematics #Separable space #Space (punctuation) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Unitary operator #Unitary state #math.FA #math.SP #msc:45P05 #msc:47G10

paper · pdf · doi:10.48550/arxiv.math/0210186

11 pages

arxiv created 2002/10/13 · openalex publication_date 2002/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we give a characterization of all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral operator in L₂(R) with bounded and arbitrarily smooth Carleman kernel on R². In addition, we give an explicit construction of corresponding unitary operators.

Related

• Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels
• Simultaneous unitary equivalence to Carleman operators with arbitrarily smooth kernels
• Simultaneous unitary equivalence to bi-Carleman operators with arbitrarily smooth kernels of Mercer type
• Integral operators with infinitely smooth bi-Carleman kernels of Mercer type
• An extension of Mercer's theorem to unbounded operators