Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 78
Page 1309
... condition , which is necessarily a boundary condition at a . It is easily seen from the preceding equation and Definition XII.4.25 that the most general symmetric boundary condition is af ' ( a ) + ßf ( a ) = 0 with a and ẞ real . Thus ...
... condition , which is necessarily a boundary condition at a . It is easily seen from the preceding equation and Definition XII.4.25 that the most general symmetric boundary condition is af ' ( a ) + ßf ( a ) = 0 with a and ẞ real . Thus ...
Page 1310
... condition must be a boundary condition at a . Hence it is clear from the above table that there is exactly one solution y of ( 7-2 ) = 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution ...
... condition must be a boundary condition at a . Hence it is clear from the above table that there is exactly one solution y of ( 7-2 ) = 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution ...
Page 1479
... condition ( if any ) at a defining T , and let By denote the boundary condition f ( N ) = 0. By remark ( b ) preceding Lemma 41 , the operator Ty obtained from the restriction Ty of t to the interval ( a , N ] by imposition of the ...
... condition ( if any ) at a defining T , and let By denote the boundary condition f ( N ) = 0. By remark ( b ) preceding Lemma 41 , the operator Ty obtained from the restriction Ty of t to the interval ( a , N ] by imposition of the ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 other sections not shown
Other editions - View all
Common terms and phrases
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 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 PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero