Linear Operators: Spectral theory |
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Page 1268
... unbounded self adjoint operators . His fundamental paper ( von Neumann [ 7 ] ) develops the theory of unbounded operators in a very complete and systematic fashion this paper is truly a classic . Von Neumann was soon joined in his work ...
... unbounded self adjoint operators . His fundamental paper ( von Neumann [ 7 ] ) develops the theory of unbounded operators in a very complete and systematic fashion this paper is truly a classic . Von Neumann was soon joined in his work ...
Page 1269
... unbounded operators . According to von Neumann [ 7 ; p . 72 ] , the notion of an unbounded self adjoint operator is due to Erhard Schmidt , who observed ( von Neumann [ 7 ; p . 62 ] ) that it is necessary to restrict one's attention to ...
... unbounded operators . According to von Neumann [ 7 ; p . 72 ] , the notion of an unbounded self adjoint operator is due to Erhard Schmidt , who observed ( von Neumann [ 7 ; p . 62 ] ) that it is necessary to restrict one's attention to ...
Page 1278
... unbounded . Consequently , the problem of choosing a domain for a differential operator is by no means trivial ; the study of symmetric unbounded operators in Section XII.4 indicates that for unbounded operators , the choice of domains ...
... unbounded . Consequently , the problem of choosing a domain for a differential operator is by no means trivial ; the study of symmetric unbounded operators in Section XII.4 indicates that for unbounded operators , the choice of domains ...
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