Linear Operators: Spectral theory |
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Page 1844
... linear space with an inner product . Duke Math . J. 5 , 520-534 ( 1939 ) . 2. On the supporting - plane property of ... linear transformations . Bull . Amer . Math . Soc . 48 , 76–93 ( 1942 ) . Linear transformations between Hilbert ...
... linear space with an inner product . Duke Math . J. 5 , 520-534 ( 1939 ) . 2. On the supporting - plane property of ... linear transformations . Bull . Amer . Math . Soc . 48 , 76–93 ( 1942 ) . Linear transformations between Hilbert ...
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
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 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 PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero