The Spectrum and Pseudospectrum of Non-self Adjoint Pseudodifferential Operators
نویسندگان
چکیده
منابع مشابه
Non-self-adjoint Differential Operators
We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find 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 instability of the eigenvalues under small perturbations of the opera...
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The theory of pseudospectra has grown rapidly since its emergence from within numerical analysis around 1990. We describe some of its applications to the stability theory of differential operators, to WKB analysis and even to orthogonal polynomials. Although currently more a way of looking at non-self-adjoint operators than a list of theorems, its future seems to be assured by the growing numbe...
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Self-adjoint operators and their spectra play a crucial rôle in analysis and physics. For instance, in quantum physics self-adjoint operators are used to describe measurements and the spectrum represents the set of possible measurement results. Therefore, it is a natural question whether the spectrum of a self-adjoint operator can be computed from a description of the operator. We prove that gi...
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We consider the long standing open question on whether one can actually compute spectra and pseudospectra of arbitrary (possibly non-self-adjoint) Schrödinger operators.We conclude that the answer is affirmative for “almost all” such operators, meaning that the operators must satisfy rather weak conditions such as the spectrum cannot be empty nor the whole plane. We include algorithms for the g...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2010
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2010.v6.n3.a9