Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1301
... independent of the set 4o , ... , 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 4o , ... , 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 ( t - λ ) 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 ( t - λ ) 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 ) i 1 , . . . , k ; i.e. , T is the restriction of T1 ( T ) ( cf. Definition ... independent boundary conditions defining T is equal to the number of linearly independent solutions of the equation ...
... independent boundary conditions B , ( f ) i 1 , . . . , k ; i.e. , T is the restriction of T1 ( T ) ( cf. Definition ... independent boundary conditions defining T is equal to the number of linearly independent solutions of the equation ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero