Linear Operators: Spectral theory |
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Page 1626
... theories . A number of other applications of linear analysis to the study of differential operators besides the spectral theory presented in the present chapter have recently received attention . Two of these theories seem particularly ...
... theories . A number of other applications of linear analysis to the study of differential operators besides the spectral theory presented in the present chapter have recently received attention . Two of these theories seem particularly ...
Page 1813
... theory of systems of linear differential equations in a one - dimensional domain , I , II . I. Mat . Sbornik N. S. 18 ( 60 ) , 305-328 ( 1946 ) . II . ibid . 21 ( 63 ) , 143–159 ( 1947 ) . ( Russian . English summary ) Math . Rev. 8 ...
... theory of systems of linear differential equations in a one - dimensional domain , I , II . I. Mat . Sbornik N. S. 18 ( 60 ) , 305-328 ( 1946 ) . II . ibid . 21 ( 63 ) , 143–159 ( 1947 ) . ( Russian . English summary ) Math . Rev. 8 ...
Page 1815
... Theory . D. van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . 7. Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press ...
... Theory . D. van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . 7. Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero