Linear Operators: Spectral theory |
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Page 926
... gives a thorough discussion of spectral theory in a separable Hilbert space , and is a very valuable reference ; it is ... give only very brief remarks concerning the results presented in the text . This will enable us to comment on ...
... gives a thorough discussion of spectral theory in a separable Hilbert space , and is a very valuable reference ; it is ... give only very brief remarks concerning the results presented in the text . This will enable us to comment on ...
Page 937
... give anything approaching an exhaustive treatment of the subjects considered . However , due to the comprehensiveness and power of the general spectral theory , it is possible not only to give a satisfactory foundation for these ...
... give anything approaching an exhaustive treatment of the subjects considered . However , due to the comprehensiveness and power of the general spectral theory , it is possible not only to give a satisfactory foundation for these ...
Page 1163
... gives some results for a class of integral operators defined by requiring the finiteness of integral expressions in the kernel then generalizing the Hilbert - Schmidt requirement SfK ( x , y ) \ 2dxdy < ∞ . Exercises 25 through 36 give ...
... gives some results for a class of integral operators defined by requiring the finiteness of integral expressions in the kernel then generalizing the Hilbert - Schmidt requirement SfK ( x , y ) \ 2dxdy < ∞ . Exercises 25 through 36 give ...
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