(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators
نویسندگان
چکیده
منابع مشابه
Non–self–adjoint Fourth–order Dissipative Operators and the Completeness of Their Eigenfunctions
A class of non-self-adjoint fourth order differential operators with general separated boundary conditions in Weyl’s limit circle case is studied. The dissipation property of the considered operators in L2[a,b) is proven by analysis and by using the characteristic determinant, the completeness of the system of eigenfunctions and associated functions of these dissipative operators also be proven...
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This agrees with the definition of the spectrum in the matrix case, where the resolvent set comprises all complex numbers that are not eigenvalues. In terms of its spectrum, we will see that a compact operator behaves like a matrix, in the sense that its spectrum is the union of all of its eigenvalues and 0. We begin with the eigenspaces of a compact operator. We start with two lemmas that we w...
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Let V be a finite-dimensional vector space, either real or complex, and equipped with an inner product 〈· , ·〉. Let A : V → V be a linear operator. Recall that the adjoint of A is the linear operator A : V → V characterized by 〈Av, w〉 = 〈v, Aw〉 ∀v, w ∈ V (0.1) A is called self-adjoint (or Hermitian) when A = A. Spectral Theorem. If A is self-adjoint then there is an orthonormal basis (o.n.b.) o...
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ژورنال
عنوان ژورنال: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2019
ISSN: 1364-503X,1471-2962
DOI: 10.1098/rsta.2019.0112