Linear Operators: Spectral theory |
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Page 1852
... linear transformations . Proc . Amer . Math . Soc . 2 , 234-237 ( 1951 ) . Semi - groups of operators . Bull . Amer . Math . Soc . 61 , 16-33 ( 1955 ) . An inversion formula for Laplace transforms and semi - groups of linear operators ...
... linear transformations . Proc . Amer . Math . Soc . 2 , 234-237 ( 1951 ) . Semi - groups of operators . Bull . Amer . Math . Soc . 61 , 16-33 ( 1955 ) . An inversion formula for Laplace transforms and semi - groups of linear operators ...
Page 1877
... linear functionals to summability . Trans . Amer . Math . Soc . 67 , 59-68 ( 1949 ) . Wilder , C. E. 1 . 2 . Expansion problems of ordinary linear differential equations with auxiliary conditions at more than two points . Trans . Amer ...
... linear functionals to summability . Trans . Amer . Math . Soc . 67 , 59-68 ( 1949 ) . Wilder , C. E. 1 . 2 . Expansion problems of ordinary linear differential equations with auxiliary conditions at more than two points . Trans . Amer ...
Page 1912
... Linear dimension , ( 91 ) Linear functional , ( 38 ) . ( See also Functional ) Linear manifold , ( 36 ) . ( See also Mani- fold ) Linear operator , ( 36 ) . ( See also B- space ) Linear space , I.11 normed , II.3.1 ( 59 ) . ( See also B ...
... Linear dimension , ( 91 ) Linear functional , ( 38 ) . ( See also Functional ) Linear manifold , ( 36 ) . ( See also Mani- fold ) Linear operator , ( 36 ) . ( See also B- space ) Linear space , I.11 normed , II.3.1 ( 59 ) . ( See also B ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero