Linear Operators, Part 2 |
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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 . 7. 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 . 7. 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 ...
Page 1880
... transformations and their resolvents in Orlicz and Lebesgue spaces . Compositio Math . 10 , 56-94 ( 1952 ) . Normalisable transformations in Hilbert space and systems of linear integral equations . Acta Math . 83 , 197-248 ( 1950 ) ...
... transformations and their resolvents in Orlicz and Lebesgue spaces . Compositio Math . 10 , 56-94 ( 1952 ) . Normalisable transformations in Hilbert space and systems of linear integral equations . Acta Math . 83 , 197-248 ( 1950 ) ...
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 domain 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 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 tr(T transform unique unitary vanishes vector zero