Linear Operators: Spectral theory |
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Page 1305
... boundary condition . A set of boundary conditions is said to be separated if it ( or , more generally , some set of boundary conditions equivalent to it ) contains no mixed boundary conditions . In all other cases the set is said to be ...
... boundary condition . A set of boundary conditions is said to be separated if it ( or , more generally , some set of boundary conditions equivalent to it ) contains no mixed boundary conditions . In all other cases the set is said to be ...
Page 1310
... conditions . Let 20. Then the boundary conditions are real , and there is exactly one solution ( t , λ ) of ( t − λ ) p = 0 square - integrable at a and satisfying the boundary conditions at a , and exactly one solution y ( t , λ ) of ...
... conditions . Let 20. Then the boundary conditions are real , and there is exactly one solution ( t , λ ) of ( t − λ ) p = 0 square - integrable at a and satisfying the boundary conditions at a , and exactly one solution y ( t , λ ) of ...
Page 1321
... boundary conditions defining T. PROOF . We have seen in the derivation of Theorem 8 that the functions a , ( t ) and ẞ , ( t ) are uniquely determined by the jump equa- tions and by the boundary conditions B ( K ) = 0 , i = 1 ...
... boundary conditions defining T. PROOF . We have seen in the derivation of Theorem 8 that the functions a , ( t ) and ẞ , ( t ) are uniquely determined by the jump equa- tions and by the boundary conditions B ( K ) = 0 , i = 1 ...
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