Linear Operators: Spectral operators |
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Page 2299
... sufficiently large and for μ in C1 , we have | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , -m 1 00 ≤ 2M dñ1 Σ ( λn | + d „ ) TM o dñm TM ( 2M | A | ) TM m = 1 ≤ 8M2 | A | d2 ( λn | + dn ) ...
... sufficiently large and for μ in C1 , we have | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , -m 1 00 ≤ 2M dñ1 Σ ( λn | + d „ ) TM o dñm TM ( 2M | A | ) TM m = 1 ≤ 8M2 | A | d2 ( λn | + dn ) ...
Page 2300
... sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E „ ) = 0 if μ is not one of the points μ ,, n ≥ K. It follows from Lemma 3 that o ( T + P ) consists of the union of the ...
... sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E „ ) = 0 if μ is not one of the points μ ,, n ≥ K. It follows from Lemma 3 that o ( T + P ) consists of the union of the ...
Page 2394
... sufficiently small μ € P + , such that σ , and og are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σз ( t , μ ) ~ e - itu ; σ ' ' ( t , μ ) ~ —iμe - itu ; as t → ∞ , for all μ Є P✦ such that I ( μ ) ...
... sufficiently small μ € P + , such that σ , and og are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σз ( t , μ ) ~ e - itu ; σ ' ' ( t , μ ) ~ —iμe - itu ; as t → ∞ , for all μ Є P✦ such that I ( μ ) ...
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