Linear Operators: Spectral operators |
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Page 1989
... spectral measure in 5 , and thus , since F is unitary , the measure e ( σ ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e ...
... spectral measure in 5 , and thus , since F is unitary , the measure e ( σ ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e ...
Page 2107
... measure μ on X to A we mean a mapping 8 → μ ( S ) from the Baire field ( the o - field generated by the compact G , sets in X ) of X into A which is weakly countably additive and satisfies μ ... spectral measure XV.16 2107 NOTES AND REMARKS.
... measure μ on X to A we mean a mapping 8 → μ ( S ) from the Baire field ( the o - field generated by the compact G , sets in X ) of X into A which is weakly countably additive and satisfies μ ... spectral measure XV.16 2107 NOTES AND REMARKS.
Page 2110
... measure space and denote L2 = L „ ( S , Σ , μ ) . Let 1 ≤r ≤ 8 ≤ + ∞ and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and T , TL , is spectral , then its resolution of the ...
... measure space and denote L2 = L „ ( S , Σ , μ ) . Let 1 ≤r ≤ 8 ≤ + ∞ and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and T , TL , is spectral , then its resolution of the ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero