Linear Operators: Spectral theory |
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Page 1178
... vector- valued functions . Let M be the mapping in L „ ( l1⁄22 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function whose nth component has the Fourier transform ...
... vector- valued functions . Let M be the mapping in L „ ( l1⁄22 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function whose nth component has the Fourier transform ...
Page 1837
... vector spaces . Trans . Amer . Math . Soc . 49 , 18-40 ( 1941 ) . Means of iterated transformations in reflexive vector spaces . Bull . Amer . Math . Soc . 45 , 945-957 ( 1939 ) . The structure of normed abelian rings . Bull . Amer ...
... vector spaces . Trans . Amer . Math . Soc . 49 , 18-40 ( 1941 ) . Means of iterated transformations in reflexive vector spaces . Bull . Amer . Math . Soc . 45 , 945-957 ( 1939 ) . The structure of normed abelian rings . Bull . Amer ...
Page 1849
... vector lattices , I , II . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217-234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . Some general theorems and convergence theorems in vector lattices . J ...
... vector lattices , I , II . I. J. Sci . Hirosima Univ . Ser . A. 12 , 17-35 ( 1942 ) . II . ibid . 12 , 217-234 ( 1943 ) . ( Japanese ) Math . Rev. 10 , 545 ( 1949 ) . Some general theorems and convergence theorems in vector lattices . J ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero