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- W2022762679 abstract "The Carleman operator is defined as the integral operator with kernel (t + s)−1 in the space $${L^2 ({mathbb R}_{+}) }$$ . This is the simplest example of a Hankel operator which can be explicitly diagonalized. Here we study a class of self-adjoint Hankel operators (we call them quasi-Carleman operators) generalizing the Carleman operator in various directions. We find explicit formulas for the total number of negative eigenvalues of the quasi-Carleman operators and, in particular, necessary and sufficient conditions for their positivity. Our approach relies on the concepts of the sigma-function and of the quasi-diagonalization of Hankel operators introduced in the preceding paper of the author." @default.
- W2022762679 created "2016-06-24" @default.
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- W2022762679 date "2014-09-03" @default.
- W2022762679 modified "2023-10-11" @default.
- W2022762679 title "Quasi-Carleman Operators and Their Spectral Properties" @default.
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- W2022762679 doi "https://doi.org/10.1007/s00020-014-2179-0" @default.
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