Linear Operators: Spectral theory |
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Page 853
... Section IV.4 , as an appended section on Hilbert space immediately following Chapter XIV . This appended section gives basic defi- nitions and the geometric properties of Hilbert space which are used repeatedly in this volume . Thus ...
... Section IV.4 , as an appended section on Hilbert space immediately following Chapter XIV . This appended section gives basic defi- nitions and the geometric properties of Hilbert space which are used repeatedly in this volume . Thus ...
Page 1392
... Section 8 below . In that section we shall first develop a part of the theory of " special functions , " and on the basis of this theory , will discuss a number of famous complete orthonormal sets , unitary integral transformations ...
... Section 8 below . In that section we shall first develop a part of the theory of " special functions , " and on the basis of this theory , will discuss a number of famous complete orthonormal sets , unitary integral transformations ...
Page 1590
... Section 5. The historical development of the main theorems in this section has been sketched in the first section of these notes . We recall that alternate proofs of these results are due to Weyl [ 5 ] ( for the operator of second order ...
... Section 5. The historical development of the main theorems in this section has been sketched in the first section of these notes . We recall that alternate proofs of these results are due to Weyl [ 5 ] ( for the operator of second order ...
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