Linear Operators: Spectral theory |
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Page 1301
... independent of the set Ao , ... , An - 1 and hence has at least n + 1 independent boundary values at a . But this is impossible by Corollary 22. Q.E.D. 24 COROLLARY . ( Weyl - Kodaira ) Let τ be a formally self adjoint formal ...
... independent of the set Ao , ... , An - 1 and hence has at least n + 1 independent boundary values at a . But this is impossible by Corollary 22. Q.E.D. 24 COROLLARY . ( Weyl - Kodaira ) Let τ be a formally self adjoint formal ...
Page 1306
... independent solutions of ( 7-2 ) σ = 0 square integrable at a or b when ( 2 ) 0. There are four possibilities as shown by the discussion above . Number of linearly independent solutions square - integrable : ( i ) ( ii ) ( iii ) ( iv ) ...
... independent solutions of ( 7-2 ) σ = 0 square integrable at a or b when ( 2 ) 0. There are four possibilities as shown by the discussion above . Number of linearly independent solutions square - integrable : ( i ) ( ii ) ( iii ) ( iv ) ...
Page 1311
... independent boundary conditions B. ( f ) 0 , i 1 , ... , k ; i.e. , T is the restriction of T1 ( 7 ) ( cf ... independent boundary conditions defining T is equal to the number of linearly independent solutions of the equation rf = 0 ...
... independent boundary conditions B. ( f ) 0 , i 1 , ... , k ; i.e. , T is the restriction of T1 ( 7 ) ( cf ... independent boundary conditions defining T is equal to the number of linearly independent solutions of the equation rf = 0 ...
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