Linear Operators: Spectral operators |
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Page 2391
... lemma . Q.E.D. 1 + 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < λ1 < ∞ . Suppose in the notation of Lemma 4 that A * ( λ1 ) # 0 , A ̄ ( λ1 ) ‡ 0 . Then for λ = λ , lying on any sufficiently short transversal to ...
... lemma . Q.E.D. 1 + 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < λ1 < ∞ . Suppose in the notation of Lemma 4 that A * ( λ1 ) # 0 , A ̄ ( λ1 ) ‡ 0 . Then for λ = λ , lying on any sufficiently short transversal to ...
Page 2396
... Lemma 1 ( cf. the graph following formula ( 14 ) ) that = 0 , lim f ( t ) = 0 , uniformly for 0≤t < 0 . 141400 μEP + Hence , by formula ( 24 ) of the proof of Lemma 3 , ĝu ( t ) ~ e - itu ; ĝu ( t ) = ―ipe - tuƒ „ ( t ) + eituƒ „ ( t ) ...
... Lemma 1 ( cf. the graph following formula ( 14 ) ) that = 0 , lim f ( t ) = 0 , uniformly for 0≤t < 0 . 141400 μEP + Hence , by formula ( 24 ) of the proof of Lemma 3 , ĝu ( t ) ~ e - itu ; ĝu ( t ) = ―ipe - tuƒ „ ( t ) + eituƒ „ ( t ) ...
Page 2479
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to 5 of the operator H of Lemma 15 ( cf. ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace H1 , and put V = V2Q . Plainly , V is symmetric ...
... Lemma 15 , while equally plainly H2 may be regarded as the restriction to 5 of the operator H of Lemma 15 ( cf. ( 33 ) – ( 36 ) above ) . Let Q be the projection of H ' onto its subspace H1 , and put V = V2Q . Plainly , V is symmetric ...
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