Linear Operators, Part 2 |
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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 4 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 4 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 , 1 R = fe L1 ( R ) . The converse part of Theorem 3.11 shows that such a character determines ...
... 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 , 1 R = fe L1 ( R ) . The converse part of Theorem 3.11 shows that such a character determines ...
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 | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero