Linear Operators: Spectral theory |
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Page 1349
... theory of positive matrix measures presented above . Definition 6 must be generalized as follows . 12 DEFINITION . Let A be an open interval of the real line , and let { μ ,, } , 1 ≤ i , j ≤n , be a family of complex valued set ...
... theory of positive matrix measures presented above . Definition 6 must be generalized as follows . 12 DEFINITION . Let A be an open interval of the real line , and let { μ ,, } , 1 ≤ i , j ≤n , be a family of complex valued set ...
Page 1392
... theory of " special functions , " and on the basis of this theory , will discuss a number of famous complete orthonormal sets , unitary integral transformations , etc. = = 6. Qualitative Theory of the Deficiency Index The methods ...
... theory of " special functions , " and on the basis of this theory , will discuss a number of famous complete orthonormal sets , unitary integral transformations , etc. = = 6. Qualitative Theory of the Deficiency Index The methods ...
Page 1872
... theory of linear semi - ordered spaces . Lening- grad State Univ . Annals [ Učenye Zapiski ] Math . Ser . 10 , 64–83 ( 1940 ) . ( Russian ) Math . Rev. 2 , 314 ( 1941 ) . Ulam , S. ( see Mazur , S. , and Oxtoby , J. C. ) Umegaki , H ...
... theory of linear semi - ordered spaces . Lening- grad State Univ . Annals [ Učenye Zapiski ] Math . Ser . 10 , 64–83 ( 1940 ) . ( Russian ) Math . Rev. 2 , 314 ( 1941 ) . Ulam , S. ( see Mazur , S. , and Oxtoby , J. C. ) Umegaki , H ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero