Linear Operators: Spectral theory |
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Page 1831
... Sbornik N. S. 33 ( 75 ) , 597-626 ( 1953 ) . ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . The theory of self - adjoint extensions of semi - bounded Hermitian operators and its applications , I , II . I. Mat . Sbornik N. S. 20 ( 62 ) ...
... Sbornik N. S. 33 ( 75 ) , 597-626 ( 1953 ) . ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . The theory of self - adjoint extensions of semi - bounded Hermitian operators and its applications , I , II . I. Mat . Sbornik N. S. 20 ( 62 ) ...
Page 1865
... Sbornik N. S. 15 ( 57 ) , 343–346 ( 1944 ) . ( Russian . English summary ) Math . Rev. 6 , 276 ( 1945 ) . Isometric operators with infinite deficiency indices and their orthogonal extensions . Doklady Akad . Nauk SSSR ( N. S. ) 87 , 11 ...
... Sbornik N. S. 15 ( 57 ) , 343–346 ( 1944 ) . ( Russian . English summary ) Math . Rev. 6 , 276 ( 1945 ) . Isometric operators with infinite deficiency indices and their orthogonal extensions . Doklady Akad . Nauk SSSR ( N. S. ) 87 , 11 ...
Page 1873
... ( N. S. ) 26 , 850-854 ( 1940 ) . Sur les propriétés du produit et de l'élément inverse dans les espaces semi ... Sbornik N. S. 22 ( 64 ) , 27–78 ( 1948 ) . ( Russian ) Math . Rev. 10 , 46 ( 1949 ) . The product in linear partially ordered ...
... ( N. S. ) 26 , 850-854 ( 1940 ) . Sur les propriétés du produit et de l'élément inverse dans les espaces semi ... Sbornik N. S. 22 ( 64 ) , 27–78 ( 1948 ) . ( Russian ) Math . Rev. 10 , 46 ( 1949 ) . The product in linear partially ordered ...
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