Linear Operators, Part 2 |
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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 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 [ SK ( x , y ) 2dxdy < ∞o . 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 [ SK ( x , y ) 2dxdy < ∞o . Exercises 25 through 36 give ...
Page 1694
... give us useful information on the structure of the set D ( I ) of distributions . 13 LEMMA . Let I be an open subset ... give a proof of this lemma is left to the reader as an exercise . Lemma 13 and the following lemma taken together ...
... give us useful information on the structure of the set D ( I ) of distributions . 13 LEMMA . Let I be an open subset ... give a proof of this lemma is left to the reader as an exercise . Lemma 13 and the following lemma taken together ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero