Linear Operators: Spectral theory |
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Page 1809
... Proc . Japan Acad . 27 , 321-327 ( 1951 ) . On a theorem of Gelfand and Neumark and the B * -algebra . Kumamoto J. Sci . Ser . A. 1 , no . 1 , 17-22 ( 1952 ) . Fullerton , R. E. 1. On a semi - group of subsets of a linear space . Proc ...
... Proc . Japan Acad . 27 , 321-327 ( 1951 ) . On a theorem of Gelfand and Neumark and the B * -algebra . Kumamoto J. Sci . Ser . A. 1 , no . 1 , 17-22 ( 1952 ) . Fullerton , R. E. 1. On a semi - group of subsets of a linear space . Proc ...
Page 1815
... Proc . Nat . Acad . Sci . U.S.A. 32 , 156-161 ( 1946 ) . Spectra and spectral manifolds . Ann . Soc . Polon . Math ... Proc . Amer . Math . Soc . 5 , 589–595 ( 1954 ) . Halmos , P. R. , Lumer , G. , and Schäffer , J. J. 1. Square roots ...
... Proc . Nat . Acad . Sci . U.S.A. 32 , 156-161 ( 1946 ) . Spectra and spectral manifolds . Ann . Soc . Polon . Math ... Proc . Amer . Math . Soc . 5 , 589–595 ( 1954 ) . Halmos , P. R. , Lumer , G. , and Schäffer , J. J. 1. Square roots ...
Page 1845
... Proc . Imp . Acad . Tokyo 18 , 333-335 ( 1942 ) . Nakamura , M. , and Umegaki , H. 1. A remark on theorems of Stone and Bochner . Proc . Japan Acad . 27 , 506–507 ( 1951 ) . Nakano , H. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Topology and ...
... Proc . Imp . Acad . Tokyo 18 , 333-335 ( 1942 ) . Nakamura , M. , and Umegaki , H. 1. A remark on theorems of Stone and Bochner . Proc . Japan Acad . 27 , 506–507 ( 1951 ) . Nakano , H. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Topology and ...
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