Linear Operators: Spectral theory |
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Page 1786
... ibid . 11 , 200-236 ( 1950 ) . III . ibid . 12 , 84-92 ( 1951 ) . IV . ibid . 12 , 93-101 ( 1951 ) . Linear operations among bounded measurable functions , I , II . I. Ann . Soc . Polon . Math . 19 , 140-161 ( 1946 ) . II . ibid . 19 ...
... ibid . 11 , 200-236 ( 1950 ) . III . ibid . 12 , 84-92 ( 1951 ) . IV . ibid . 12 , 93-101 ( 1951 ) . Linear operations among bounded measurable functions , I , II . I. Ann . Soc . Polon . Math . 19 , 140-161 ( 1946 ) . II . ibid . 19 ...
Page 1870
... ibid . 201 , 473-479 ( 1950 ) . III . ibid . 207 , 321-328 ( 1951 ) . IV . ibid . 210 , 30-47 ( 1951 ) . Introduction to the theory of Fourier integrals . Oxford Univ . Press , 1937 . Weber's integral theorem . Proc . London Math . Soc ...
... ibid . 201 , 473-479 ( 1950 ) . III . ibid . 207 , 321-328 ( 1951 ) . IV . ibid . 210 , 30-47 ( 1951 ) . Introduction to the theory of Fourier integrals . Oxford Univ . Press , 1937 . Weber's integral theorem . Proc . London Math . Soc ...
Page 1879
... ibid . 20 , 71-73 ( 1944 ) . IV . ibid . 20 , 183-185 ( 1944 ) . V. ibid . 20 , 269-273 ( 1944 ) . VI . ibid . 20 , 451-453 ( 1944 ) . Yosida , K. , and Fukamiya , M. 1. On regularly convex sets . Proc . Imp . Acad . Tokyo 17 , 49-52 ...
... ibid . 20 , 71-73 ( 1944 ) . IV . ibid . 20 , 183-185 ( 1944 ) . V. ibid . 20 , 269-273 ( 1944 ) . VI . ibid . 20 , 451-453 ( 1944 ) . Yosida , K. , and Fukamiya , M. 1. On regularly convex sets . Proc . Imp . Acad . Tokyo 17 , 49-52 ...
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