Results 171 to 180 of about 103,519 (218)

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 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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Self-Adjoint Operator Polynomials

1989
Let x be a Hilbert space with the scalar product ; x,y ∈ x. In this chapter we consider monic operator polynomials . $$ L\left( \lambda \right) = \mathop \sum \limits_{j = 0}^{\ell - 1} {\lambda ^j}{A_j} + {\lambda ^\ell }I $$ whose coefficients are (bounded) self-adjoint operators on x : Aj = A j * for j = 0,…,l-1.
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Anticommuting Self-Adjoint Operators

1991
For non-degenerate bounded self-adjoint operators A and B the relation $$ AB - \alpha BA = 0\left( {\alpha \in {\mathbb{C}^1}} \right) $$ implies that α= 1 or α = -1, i.e. the operators commute or anticommute. In this chapter we study spectral questions for unbounded anticommuting self-adjoint operators.
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On Self-Adjoint Factorization of Operators

Canadian Journal of Mathematics, 1969
The main result of this paper is that every normal operator on an infinitedimensional (complex) Hilbert space ℋ is the product of four self-adjoint operators; our Theorem 4 is an actually stronger result. A large class of normal operators will be given which cannot be expressed as the product of three self-adjoint operators.This work was motivated by a
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Unbounded Self-Adjoint Operators

2013
Recall that most of the operators of quantum mechanics, including those representing position, momentum, and energy, are not defined on the entirety of the relevant Hilbert space, but only on a dense subspace thereof.
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