Linear Operators: Spectral theory |
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Page 875
... shown that the homomorphism x → x ( · ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 4 ) of all continuous functions on the structure space △ of X is an iso- metric isomorphism of X onto all of C ( 4 ) . It ...
... shown that the homomorphism x → x ( · ) ( see Theorem 2.9 ) of a commutative B * -algebra X into the algebra C ( 4 ) of all continuous functions on the structure space △ of X is an iso- metric isomorphism of X onto all of C ( 4 ) . It ...
Page 981
... shown in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H1 ( T ( ƒ ) ) = √2 h ( x ) f ( x ) dx , R † ε L1 ( R ) . The converse part of Theorem 3.11 shows that such a character determines a ...
... shown in the first part of the proof of Theorem 3.11 , there is a continuous character h on R with H1 ( T ( ƒ ) ) = √2 h ( x ) f ( x ) dx , R † ε L1 ( R ) . The converse part of Theorem 3.11 shows that such a character determines a ...
Page 1161
... shown by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been shown by M. Paul Malliavin that spectral synthesis is not possible for all functions on the real axis . Cf. P. Malliavin , Sur l'impossibilité de ...
... shown by L. Schwartz [ 2 ] for Euclidean space of three dimensions . It has recently been shown by M. Paul Malliavin that spectral synthesis is not possible for all functions on the real axis . Cf. P. Malliavin , Sur l'impossibilité de ...
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