Linear Operators: Spectral theory |
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Page 1217
... respectively , with measures u and μ , and multiplicity sets { e , } and { e } will be called equivalent if u μ and μ ( e , 4 , ) = 0 = μ ( e̟ „ Aễn ) for n = 1 , 2 , .... ≈ 16 THEOREM . A separable Hilbert space has an ordered ...
... respectively , with measures u and μ , and multiplicity sets { e , } and { e } will be called equivalent if u μ and μ ( e , 4 , ) = 0 = μ ( e̟ „ Aễn ) for n = 1 , 2 , .... ≈ 16 THEOREM . A separable Hilbert space has an ordered ...
Page 1326
... respectively , and which satisfy the boundary conditions at a and at b respectively . Then the resolvent R ( 2 ; T ) = ( 1 - T ) is given by the expression ( R ( 2 ; T ) f ) ( t ) = √ , f ( s ) K ( t , s ; 2 ) ds , where the kernel K ...
... respectively , and which satisfy the boundary conditions at a and at b respectively . Then the resolvent R ( 2 ; T ) = ( 1 - T ) is given by the expression ( R ( 2 ; T ) f ) ( t ) = √ , f ( s ) K ( t , s ; 2 ) ds , where the kernel K ...
Page 1548
... respectively by the boundary conditions f ( c ) = f ' ( c ) = f ( n - 1 ) ( c ) = 0 and by the boundary conditions in the set B at the right and at the left endpoints of I respectively . Show that the operators T1 and T2 are self ...
... respectively by the boundary conditions f ( c ) = f ' ( c ) = f ( n - 1 ) ( c ) = 0 and by the boundary conditions in the set B at the right and at the left endpoints of I respectively . Show that the operators T1 and T2 are self ...
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