Linear Operators: Spectral theory |
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Page 1317
... ( c , s ) = Σα , ( c ) p ( s ) , 8 < c , i = 1 Q * Σβ . ( c ) Ψ . ( 8 ) , * s > c . i = 1 The p * + q * constants a , ( c ) and B , ( c ) will now be computed . Consider then linear equations [ 1 ] K ( c , c + 0 ) -K ( c , c − 0 ) = 0 ...
... ( c , s ) = Σα , ( c ) p ( s ) , 8 < c , i = 1 Q * Σβ . ( c ) Ψ . ( 8 ) , * s > c . i = 1 The p * + q * constants a , ( c ) and B , ( c ) will now be computed . Consider then linear equations [ 1 ] K ( c , c + 0 ) -K ( c , c − 0 ) = 0 ...
Page 1638
... C ( I ) consists of those scalar functions ƒ defined on I which have all partial derivatives of all orders existing and continuous . Similarly , the set C ( I ) consists of those scalar functions defined in I every one of whose partial ...
... C ( I ) consists of those scalar functions ƒ defined on I which have all partial derivatives of all orders existing and continuous . Similarly , the set C ( I ) consists of those scalar functions defined in I every one of whose partial ...
Page 1677
... ( C ) , and a F be in H ( C ) . Let G denote an arbitrary element of H ( C ) . Then , by Definition 35 , and by the Hahn - Banach theorem ( II.3.11 ) , the mapping p → G ( q ) can be extended to a continuous linear functional ( which we ...
... ( C ) , and a F be in H ( C ) . Let G denote an arbitrary element of H ( C ) . Then , by Definition 35 , and by the Hahn - Banach theorem ( II.3.11 ) , the mapping p → G ( q ) can be extended to a continuous linear functional ( which we ...
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