Linear Operators: Spectral theory |
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Page 966
For some choice off the integral on the right of [ * ] is not zero and since , by
Lemma 1 ( d ) , the integral on the left of [ * ] is continuous , we conclude that hm
agrees almost everywhere with a continuous function . By redefining him on a set
of ...
For some choice off the integral on the right of [ * ] is not zero and since , by
Lemma 1 ( d ) , the integral on the left of [ * ] is continuous , we conclude that hm
agrees almost everywhere with a continuous function . By redefining him on a set
of ...
Page 968
... is a topological group . PROOF . Verification that the neighborhoods N ( h , K ,
€ ) are a base for a topology will be left to the reader . If h , e N ( h , K , e ) and h ,
E N ( ho , K , 8 ) then hy h2 EN ( hho , K2 , ε ) so that multiplication is continuous .
... is a topological group . PROOF . Verification that the neighborhoods N ( h , K ,
€ ) are a base for a topology will be left to the reader . If h , e N ( h , K , e ) and h ,
E N ( ho , K , 8 ) then hy h2 EN ( hho , K2 , ε ) so that multiplication is continuous .
Page 1903
6 ( 428 ) criteria for existence of continuous linear functionals , V . 7 . 3 ( 436 ) non
- existence in Lp , 0 < p < 1 , V . 7 . 37 ( 438 ) Continuous functions . ( See also
Absolutely continuous functions ) as a B - space , additional properties , IV .
6 ( 428 ) criteria for existence of continuous linear functionals , V . 7 . 3 ( 436 ) non
- existence in Lp , 0 < p < 1 , V . 7 . 37 ( 438 ) Continuous functions . ( See also
Absolutely continuous functions ) as a B - space , additional properties , IV .
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
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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 neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero