Linear Operators: Spectral theory |
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Page 1797
... transformations in Hilbert space . Duke J. Math . 7 , 504-508 ( 1940 ) . Cameron , R. H. 1. A " Simpson's Rule " for the numerical evaluation of Wiener's integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . 4 ...
... transformations in Hilbert space . Duke J. Math . 7 , 504-508 ( 1940 ) . Cameron , R. H. 1. A " Simpson's Rule " for the numerical evaluation of Wiener's integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . 3 . 4 ...
Page 1815
... transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . Measure Theory . D. van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Finite ...
... transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . Measure Theory . D. van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Finite ...
Page 1844
... transformations . Bull . Amer . Math . Soc . 48 , 76–93 ( 1942 ) . Linear transformations between Hilbert spaces and the application of this theory to linear partial differential equations . Trans . Amer . Math . Soc . 37 , 301-338 ...
... transformations . Bull . Amer . Math . Soc . 48 , 76–93 ( 1942 ) . Linear transformations between Hilbert spaces and the application of this theory to linear partial differential equations . Trans . Amer . Math . Soc . 37 , 301-338 ...
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