Linear Operators: Spectral theory |
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Page 1786
... Math . Rev. 9 , 241 ( 1948 ) . Necessary conditions for the extension of linear operations . Doklady Akad . Nauk ... Studia Math . 14 ( 1953 ) , 79-81 ( 1954 ) . Alexandroff , A. D. 1 . Additive set functions in abstract spaces , I – III ...
... Math . Rev. 9 , 241 ( 1948 ) . Necessary conditions for the extension of linear operations . Doklady Akad . Nauk ... Studia Math . 14 ( 1953 ) , 79-81 ( 1954 ) . Alexandroff , A. D. 1 . Additive set functions in abstract spaces , I – III ...
Page 1840
... Math . Sem . Rep . 1950 , 41-44 ( 1950 ) . Masani , P. R. 1. Multiplicative Riemann integration in normed rings ... Studia Math . 4 , 70–84 ( 1933 ) . Über die kleinste konvexe Menge , die eine gegebene kompakte Menge enthält . Studia ...
... Math . Sem . Rep . 1950 , 41-44 ( 1950 ) . Masani , P. R. 1. Multiplicative Riemann integration in normed rings ... Studia Math . 4 , 70–84 ( 1933 ) . Über die kleinste konvexe Menge , die eine gegebene kompakte Menge enthält . Studia ...
Page 1850
... Studia Math . 4 , 33-37 ( 1933 ) . II . ibid . 4 , 41-47 ( 1933 ) . 2. Über konjugierte Exponentenfolgen . Studia Math . 3 , 200-211 ( 1931 ) Über eine gewisse Klasse von Räumen von Typus B. Bull . Int . Acad . Polon Sci . Sér . A ...
... Studia Math . 4 , 33-37 ( 1933 ) . II . ibid . 4 , 41-47 ( 1933 ) . 2. Über konjugierte Exponentenfolgen . Studia Math . 3 , 200-211 ( 1931 ) Über eine gewisse Klasse von Räumen von Typus B. Bull . Int . Acad . Polon Sci . Sér . A ...
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