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 B1 ( x ) 1 , ... , k , and we have only to show that k = n ...
... 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 B1 ( x ) 1 , ... , k , and we have only to show that k = n ...
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 1548
... adjoint operators T and ↑ as in Exercise D2 . Show that λ „ ( T ) ≥ λ ... extension of T。( 7 ) defined by a separated set B of boundary conditions ... adjoint . Let 2 , ( T ) , λ „ ( T1 ) and λ „ ( T2 ) be the numbers of Exercise D2 as ...
... adjoint operators T and ↑ as in Exercise D2 . Show that λ „ ( T ) ≥ λ ... extension of T。( 7 ) defined by a separated set B of boundary conditions ... adjoint . Let 2 , ( T ) , λ „ ( T1 ) and λ „ ( T2 ) be the numbers of Exercise D2 as ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero