Linear Operators: Spectral theory |
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Page 1830
... ( Russian ) Math . Rev. 14 , 55 ( 1953 ) . Kramer , H. P. 1 . Perturbation of differential operators . Dissertation ... ( Russian ) Math . Rev. 13 , 47 ( 1952 ) . On self - adjoint extensions of Hermitian operators . Ukrain . Mat . Ž . 1 ...
... ( Russian ) Math . Rev. 14 , 55 ( 1953 ) . Kramer , H. P. 1 . Perturbation of differential operators . Dissertation ... ( Russian ) Math . Rev. 13 , 47 ( 1952 ) . On self - adjoint extensions of Hermitian operators . Ukrain . Mat . Ž . 1 ...
Page 1831
... ( Russian ) Math . Rev. 11 , 670 ( 1950 ) . On the trace formula in perturbation theory . Mat . Sbornik N. S. 33 ( 75 ) , 597-626 ( 1953 ) . ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . The theory of self - adjoint extensions of semi ...
... ( Russian ) Math . Rev. 11 , 670 ( 1950 ) . On the trace formula in perturbation theory . Mat . Sbornik N. S. 33 ( 75 ) , 597-626 ( 1953 ) . ( Russian ) Math . Rev. 15 , 720 ( 1954 ) . The theory of self - adjoint extensions of semi ...
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 ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero