Linear Operators, Part 2 |
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Page 1191
... operator is not self adjoint for it is clear from the above equations that any function g with a continuous first ... adjoint of id / dt . The problem , suggested by the preceding example , of finding self adjoint extensions of a given ...
... operator is not self adjoint for it is clear from the above equations that any function g with a continuous first ... adjoint of id / dt . The problem , suggested by the preceding example , of finding self adjoint extensions of a given ...
Page 1270
... operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important to know what the self adjoint extensions look ...
... operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important to know what the self adjoint extensions look ...
Page 1290
... operator n d i dt d Σ ( -1 ) ( 1 ) P « ) ( 1 ) i = 0 Pi ( t ) is formally self adjoint provided only that the coefficients pi are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ...
... operator n d i dt d Σ ( -1 ) ( 1 ) P « ) ( 1 ) i = 0 Pi ( t ) is formally self adjoint provided only that the coefficients pi are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 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 open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero