Linear Operators, Part 2 |
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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 extensions of the operator T = dt 2 + g ( t ) , 0 ≤t≤ then the function q is uniquely determined . Levinson [ 4 ] simplified Borg's arguments , and proved that the distribution of eigenvalues of one self adjoint extension ...
... adjoint extensions of the operator T = dt 2 + g ( t ) , 0 ≤t≤ then the function q is uniquely determined . Levinson [ 4 ] simplified Borg's arguments , and proved that the distribution of eigenvalues of one self adjoint extension ...
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 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 real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero