Linear Operators: Spectral theory |
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Page 1218
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , g | d are continuous then so is the restriction ( af + Bg ) on 8 and thus the class of measurable functions having the required property is a ...
... restriction of f to the complement of o is continuous . PROOF . If the restrictions fo , g | d are continuous then so is the restriction ( af + Bg ) on 8 and thus the class of measurable functions having the required property is a ...
Page 1471
... restriction of T1 ( 71 ) defined by a boundary condition f ( t ) + cf ' ( t ) = 0 and by the boundary condition B ( ƒ ) = 0 ( if has any boundary values at a ) , then S * is the restriction of T1 ( T1 ) defined by the boundary condition ...
... restriction of T1 ( 71 ) defined by a boundary condition f ( t ) + cf ' ( t ) = 0 and by the boundary condition B ( ƒ ) = 0 ( if has any boundary values at a ) , then S * is the restriction of T1 ( T1 ) defined by the boundary condition ...
Page 1613
... restriction of T1 ( t , X ) , the remaining part of the spectrum depends on the restriction chosen , and may lie in the residual spectrum and / or the point spectrum or in the resolvent set of the restricted operator . The main problem ...
... restriction of T1 ( t , X ) , the remaining part of the spectrum depends on the restriction chosen , and may lie in the residual spectrum and / or the point spectrum or in the resolvent set of the restricted operator . The main problem ...
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