Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 926
... theory of Hermitian operators goes back to the work of Hilbert [ 1 , IV ] . Proofs of this result were also given by F. Riesz [ 20 , 6 ] , and contribu- tions were made by many others . The reader is referred to the encyclo- pedic ...
... theory of Hermitian operators goes back to the work of Hilbert [ 1 , IV ] . Proofs of this result were also given by F. Riesz [ 20 , 6 ] , and contribu- tions were made by many others . The reader is referred to the encyclo- pedic ...
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 1583
... theory of special functions , which we shall briefly touch upon later . However , the " spectral " theory which they had discovered was to wait until the first decade of this century before it was actively taken up again . It was Dini ...
... theory of special functions , which we shall briefly touch upon later . However , the " spectral " theory which they had discovered was to wait until the first decade of this century before it was actively taken up again . It was Dini ...
Contents
IX | 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero