Linear Operators: Spectral theory |
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Page 853
... Section IV.4 , as an appended section on Hilbert space immediately following Chapter XIV . This appended section gives basic defi- nitions and the geometric properties of Hilbert space which are used repeatedly in this volume . Thus ...
... Section IV.4 , as an appended section on Hilbert space immediately following Chapter XIV . This appended section gives basic defi- nitions and the geometric properties of Hilbert space which are used repeatedly in this volume . Thus ...
Page 1392
... Section 8 below . In that section we shall first develop a part of the theory of " special functions , " and on the basis of this theory , will discuss a number of famous complete orthonormal sets , unitary integral transformations ...
... Section 8 below . In that section we shall first develop a part of the theory of " special functions , " and on the basis of this theory , will discuss a number of famous complete orthonormal sets , unitary integral transformations ...
Page 1634
... section to the statement of a series of notational conventions and abbreviations which will be of considerable use in the sections to follow . In the body of our analysis ( as in the elementary proof of local dependence given above ) we ...
... section to the statement of a series of notational conventions and abbreviations which will be of considerable use in the sections to follow . In the body of our analysis ( as in the elementary proof of local dependence given above ) we ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero