Linear Operators: Spectral operators |
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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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology unique unitary vanishes vector zero