Linear Operators: Spectral theory |
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Page 1152
... measure on a group satisfying the second axiom of countability was first shown by Haar [ 1 ] , and the question of ... positive measure if and only if R is discrete . PROOF . If R is compact then Theorem 3 implies that λ ( R ) ...
... measure on a group satisfying the second axiom of countability was first shown by Haar [ 1 ] , and the question of ... positive measure if and only if R is discrete . PROOF . If R is compact then Theorem 3 implies that λ ( R ) ...
Page 1276
... positive Borel measure on the real axis such that all the -∞ Stoo \ t \ 25 μ ( dt ) , g≥0 , converge . Is the measure μ unique ? This fundamental problem of the theory of moments may be answered as follows . Let { P , ( t ) } be the ...
... positive Borel measure on the real axis such that all the -∞ Stoo \ t \ 25 μ ( dt ) , g≥0 , converge . Is the measure μ unique ? This fundamental problem of the theory of moments may be answered as follows . Let { P , ( t ) } be the ...
Page 1341
... positive matrix measure defined on the real line , then La ( { } ) is a Hilbert space . The proof of this theorem will be based on the following lemma . 11 LEMMA . Let { μ ; } be a positive matrix measure whose elements are continuous ...
... positive matrix measure defined on the real line , then La ( { } ) is a Hilbert space . The proof of this theorem will be based on the following lemma . 11 LEMMA . Let { μ ; } be a positive matrix measure whose elements are continuous ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero