Linear Operators: Spectral theory |
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Page 1180
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions f with values in any space L ( ) , § denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
... Hilbert space . Therefore , Corollary 23 generalizes , with hardly any change in its proof , to the space of functions f with values in any space L ( ) , § denoting an arbitrary Hilbert space . Next , it may be noted that Lemma 24 ...
Page 1262
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space 1 2H , and an orthogonal projection Qin , such that Ax = PQx , x = H , P denoting the orthogonal projection of 1 on H. 29 Let { T } be a sequence of bounded ...
... Hilbert space with 0 ≤ A≤I be given . Then there exists a Hilbert space 1 2H , and an orthogonal projection Qin , such that Ax = PQx , x = H , P denoting the orthogonal projection of 1 on H. 29 Let { T } be a sequence of bounded ...
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Nelson Dunford, Jacob T. Schwartz. APPENDIX Hilbert space is a linear vector space over the field Ø of complex ... spaces , Hilbert APPENDIX REFERENCES NOTATION INDEX AUTHOR INDEX SUBJECT INDEX.
Nelson Dunford, Jacob T. Schwartz. APPENDIX Hilbert space is a linear vector space over the field Ø of complex ... spaces , Hilbert APPENDIX REFERENCES NOTATION INDEX AUTHOR INDEX SUBJECT INDEX.
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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