Linear Operators: Spectral theory |
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Page 1239
... adjoint extension of T. Then by Lemma 26 , T1 is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B ( x ) = 0 , i = 1 , . . . , k , and we have only to show ...
... adjoint extension of T. Then by Lemma 26 , T1 is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B ( x ) = 0 , i = 1 , . . . , k , and we have only to show ...
Page 1270
... 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 like and how they are ...
... 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 like and how they are ...
Page 1622
... adjoint extension of some differential operator , and of calculating this differential operator explicitly , if it ... adjoint extensions of the operator T = - d \ 2 dt + q ( t ) , 0 ≤t ≤ л , then the function q is uniquely determined ...
... adjoint extension of some differential operator , and of calculating this differential operator explicitly , if it ... adjoint extensions of the operator T = - d \ 2 dt + q ( t ) , 0 ≤t ≤ л , then the function q is uniquely determined ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero