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Page 1152
Points in R have positive measure if and only if R is discrete . Proof . If R is compact then Theorem 3 implies that a ( R ) < oo . Conversely , suppose that R is not compact , and let V be a neighborhood of the identity with compact ...
Points in R have positive measure if and only if R is discrete . Proof . If R is compact then Theorem 3 implies that a ( R ) < oo . Conversely , suppose that R is not compact , and let V be a neighborhood of the identity with compact ...
Page 1276
and that this sequence can be represented in the form € ; = so tou ( dt ) , g 20 - where u is a positive Borel measure on the real axis such that all the integrals + Sto 1412 ju ( dt ) , g 20 , converge . Is the measure j unique ?
and that this sequence can be represented in the form € ; = so tou ( dt ) , g 20 - where u is a positive Borel measure on the real axis such that all the integrals + Sto 1412 ju ( dt ) , g 20 , converge . Is the measure j unique ?
Page 1341
If { u } is an n x n positive matrix measure defined on the real line , then L2 ( { u is } ) is a Hilbert space . The proof of this theorem will be based on the following lemma . 11 LEMMA . Let { } be a positive matrix measure whose ...
If { u } is an n x n positive matrix measure defined on the real line , then L2 ( { u is } ) is a Hilbert space . The proof of this theorem will be based on the following lemma . 11 LEMMA . Let { } be a positive matrix measure whose ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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 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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero