Results 181 to 190 of about 2,806 (244)

Non‐Self‐Adjoint Differential Operators

Bulletin of the London Mathematical Society, 2002
A description is given of methods that have been used to analyze the spectrum of non‐self‐adjoint differential operators, emphasizing the differences from the self‐adjoint theory. It transpires that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of ...
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Self-Adjoint Operators and Cones

Journal of the London Mathematical Society, 1996
Summary: Suppose that \(K\) is a cone in a real Hilbert space \({\mathcal H}\) with \(K^\perp=\{0\}\), and that \(A:{\mathcal H}\to{\mathcal H}\) is a selfadjoint operator which maps \(K\) into itself. If \(|A|\) is an eigenvalue of \(A\), it is shown that it has an eigenvector in the cone.
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Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators

Journal of Fourier Analysis and Applications, 2018
We deal with homogeneous Besov and Triebel–Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property.
A. G. Georgiadis, G. Kerkyacharian, G. Kyriazis, P. Petrushev   +3 more
semanticscholar   +1 more source

Self-adjoint polynomial operator pencils, spectrally equivalent to self-adjoint operators

Ukrainian Mathematical Journal, 1985
Let \(L(\lambda)=\lambda^ nA_ 0+...+A_ n\) be an operator pencil on a Hilbert space H with \(A_ 0,...,A_ n\) selfadjoint and \(A_ 0\) invertible. Then L(\(\lambda)\) can be associated with a pencil \(\tilde L(\lambda)= \lambda\tilde I-\tilde L\) with the same spectrum, defined on a direct sum \(\tilde H\) of n copies of H. The author shows that if \(L(\
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Self-adjoint operators

2016
First we prove some fundamental results for the adjoint map (see 12.1–12.6) and then present a version of the spectral theorem 11.9 for compact normal operators (theorem 12.12). Here we employ the notation x, x’! = x, x’! X = x’(x) from 7.4. We remark that the adjoint map of an operator has already been defined in 5.5(8).
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Self-adjoint Hamilton Operators

2003
The time evolution of a classical mechanical system is governed by the Hamilton function. Similarly, the Hamilton operator determines the time evolution of a quantum mechanical system and this operator provides information about the total energy of the system in specific states.
Philippe Blanchard, Erwin Brüning
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Self-adjoint Operators and Conserved Currents

General Relativity and Gravitation, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Torres del Castillo, G. F., Flores-Urbina, J. C.   +1 more
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Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei

, 2017
We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling.
M. Gallone, A. Michelangeli
semanticscholar   +1 more source

Self-Adjoint Operators. SchrÖdinger Operators

1981
In Section 2.1 we define symmetric and self-adjoint operators and give criteria for a symmetric operator to be self-adjoint. In Section 2.2 we study simple spectral properties of self-adjoint operators. A particular class of self-adjoint operators, the socalled multiplication operators, are introduced in Section 2.3, and the results are applied to ...
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SPECTRA OF RANDOM SELF ADJOINT OPERATORS

Russian Mathematical Surveys, 1973
This survey contains an exposition of the results obtained in the studying the spectra of certain classes of random operators. It consists of three chapters. In the introductory Chapter I we survey some of the pioneering papers (two, in particular), which have sufficient depth of content to suggest the natural problems to be considered in this field ...
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