Linear Operators: Spectral theory |
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Page 937
... theory , it is possible not only to give a satisfactory foundation for these subjects , but also to develop their principal results , and this we shall attempt to do . The topics discussed are group theory and the Peter - Weyl theorem ...
... theory , it is possible not only to give a satisfactory foundation for these subjects , but also to develop their principal results , and this we shall attempt to do . The topics discussed are group theory and the Peter - Weyl theorem ...
Page 1585
... theory of differential operators of second order assumes a physically significant role . Thus the physicists of the time were naturally led to interest themselves in the theory of Weyl . But , while many of the useful insights of the ...
... theory of differential operators of second order assumes a physically significant role . Thus the physicists of the time were naturally led to interest themselves in the theory of Weyl . But , while many of the useful insights of the ...
Page 1867
... theory of representations for Boolean algebras . Trans . Amer . Math . Soc . 40 , 37-111 ( 1936 ) . Linear transformations in Hilbert space , I – III . I. Proc . Nat . Acad . Sci . U.S.A. 15 , 198-200 ( 1929 ) . II . ibid . 15 , 423-425 ...
... theory of representations for Boolean algebras . Trans . Amer . Math . Soc . 40 , 37-111 ( 1936 ) . Linear transformations in Hilbert space , I – III . I. Proc . Nat . Acad . Sci . U.S.A. 15 , 198-200 ( 1929 ) . II . ibid . 15 , 423-425 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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(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 satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero