Linear Operators, Part 2 |
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Page 1835
... ( Russian ) Math . Rev. 11 , 720 ( 1950 ) . Proof of the theorem on the expansion in eigenfunctions of self - adjoint differential operators . Doklady Akad . Nauk SSSR ( N. S. ) 73 , 651-654 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ...
... ( Russian ) Math . Rev. 11 , 720 ( 1950 ) . Proof of the theorem on the expansion in eigenfunctions of self - adjoint differential operators . Doklady Akad . Nauk SSSR ( N. S. ) 73 , 651-654 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ...
Page 1848
... ( Russian . English summary ) Math . Rev. 2 , 104 ( 1941 ) . Spectral functions of a symmetric operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 105 ( 1941 ) . On the ...
... ( Russian . English summary ) Math . Rev. 2 , 104 ( 1941 ) . Spectral functions of a symmetric operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 105 ( 1941 ) . On the ...
Page 1865
... ( Russian ) Math . Rev. 14 , 882 ( 1953 ) . Operators with degenerate characteristic functions . Doklady Akad . Nauk SSSR ( N. S. ) 93 , 985-988 ( 1953 ) . ( Russian ) Math . Rev. 15 , 803 ( 1954 ) . Completely continuous perturbations of ...
... ( Russian ) Math . Rev. 14 , 882 ( 1953 ) . Operators with degenerate characteristic functions . Doklady Akad . Nauk SSSR ( N. S. ) 93 , 985-988 ( 1953 ) . ( Russian ) Math . Rev. 15 , 803 ( 1954 ) . Completely continuous perturbations of ...
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 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