Linear Operators: Spectral theory |
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Page 1176
Let p , q , kn be as in the preceding lemma , and , for each N , let X y be the
transformation in L , ( la ) which maps the vector whose nth component has the
Fourier transform fn ( 5 ) into the vector whose nth component has the Fourier
transform ...
Let p , q , kn be as in the preceding lemma , and , for each N , let X y be the
transformation in L , ( la ) which maps the vector whose nth component has the
Fourier transform fn ( 5 ) into the vector whose nth component has the Fourier
transform ...
Page 1178
It is plain from Plancherel's theorem that X is a bounded mapping of the space Lg
of scalar - valued functions into the space L2 ( 12 ) of square - integrable vector -
valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , X ...
It is plain from Plancherel's theorem that X is a bounded mapping of the space Lg
of scalar - valued functions into the space L2 ( 12 ) of square - integrable vector -
valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , X ...
Page 1751
s differentiable m - vector valued functions defined in C. Similarly , © ( C ) and © (
C ) will denote the subspaces of Ĉ ~ ( C ) consisting of all functions which are
multiply periodic of period 27 and of all functions which vanish outside a compact
...
s differentiable m - vector valued functions defined in C. Similarly , © ( C ) and © (
C ) will denote the subspaces of Ĉ ~ ( C ) consisting of all functions which are
multiply periodic of period 27 and of all functions which vanish outside a compact
...
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Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
57 other sections not shown
Common terms and phrases
additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero