Linear Operators, Part 2 |
From inside the book
Results 1-3 of 79
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 1400
... adjoint extension T of To ( T ) , the dimension of the null - space { f \ Tf = λf } is at most k ; ( b ) there exist self adjoint extensions T of To ( t ) such that λ o ( T ) ; ( c ) there exist self adjoint extensions T of To ( t ) ...
... adjoint extension T of To ( T ) , the dimension of the null - space { f \ Tf = λf } is at most k ; ( b ) there exist self adjoint extensions T of To ( t ) such that λ o ( T ) ; ( c ) there exist self adjoint extensions T of To ( t ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 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 domain 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 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 subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero