Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 905
... operator T in § is countable then there is an orthonormal basis B for eigenvectors of ... spectral point is an eigenvalue and the number of linearly independent ... types of normal operators which occur frequently in mathematical analysis ...
... operator T in § is countable then there is an orthonormal basis B for eigenvectors of ... spectral point is an eigenvalue and the number of linearly independent ... types of normal operators which occur frequently in mathematical analysis ...
Page 1393
... operator derived from either t1 or t2 has a continuous spectrum , and that , in fact , the spectrum of each such operator consists of an infinite sequence of points approaching + ∞ . We begin by defining a certain type of " spectrum ...
... operator derived from either t1 or t2 has a continuous spectrum , and that , in fact , the spectrum of each such operator consists of an infinite sequence of points approaching + ∞ . We begin by defining a certain type of " spectrum ...
Page 1592
... type of theorem . Various related results on the topics treated in Sections ... spectral theory of the operators in this section are scattered through the ... Operator of the 1592 XIII . ORDINARY DIFFERENTIAL OPERATORS XIII.10.B.
... type of theorem . Various related results on the topics treated in Sections ... spectral theory of the operators in this section are scattered through the ... Operator of the 1592 XIII . ORDINARY DIFFERENTIAL OPERATORS XIII.10.B.
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero