On finite rank Hankel operators
Copyright policy )On finite rank Hankel operators
For self-adjoint Hankel operators of finite rank, we find an explicit formula for the total multiplicity of their negative and positive spectra. We also show that very strong perturbations, for example, a perturbation by the Carleman operator, do not change the total number of negative eigenvalues of finite rank Hankel operators.
Mathematics - Spectral Theory, Hankel operator, 47A40, sign function, total multiplicity of the positive and negative spectra, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Spectrum, resolvent, 47B25, Carleman operator, Spectral Theory (math.SP), spectral multiplicity, Necessary and sufficient conditions for the sign-definiteness, the Carleman operator and its perturbations, The sign-function, 47A40, 47B25, Functional Analysis (math.FA), Mathematics - Functional Analysis, Toeplitz operators, Hankel operators, Wiener-Hopf operators, sign definiteness
Mathematics - Spectral Theory, Hankel operator, 47A40, sign function, total multiplicity of the positive and negative spectra, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Spectrum, resolvent, 47B25, Carleman operator, Spectral Theory (math.SP), spectral multiplicity, Necessary and sufficient conditions for the sign-definiteness, the Carleman operator and its perturbations, The sign-function, 47A40, 47B25, Functional Analysis (math.FA), Mathematics - Functional Analysis, Toeplitz operators, Hankel operators, Wiener-Hopf operators, sign definiteness
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