Linear Operators: Spectral operators |
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Page 2322
... hypothesis . Πι 1 REGULARITY HYPOTHESIS For Even Order CASE . The polynomials and T2 are of order p . If Regularity Hypothesis 1 is satisfied , we may write 2322 XIX.4.1 XIX . PERTURBATIONS OF SPECTRAL OPERATORS.
... hypothesis . Πι 1 REGULARITY HYPOTHESIS For Even Order CASE . The polynomials and T2 are of order p . If Regularity Hypothesis 1 is satisfied , we may write 2322 XIX.4.1 XIX . PERTURBATIONS OF SPECTRAL OPERATORS.
Page 2342
... Hypothesis 1 , we may then assume without loss of generality that Biff ( i ) ( 0 ) for 1≤i≤v and B1f = f ( mi ) ( 1 ) for v < i≤ 2v . The matrix Ñ1 ( μ ) of the remark following Regularity Hypothesis 1 is con- sequently determined by ...
... Hypothesis 1 , we may then assume without loss of generality that Biff ( i ) ( 0 ) for 1≤i≤v and B1f = f ( mi ) ( 1 ) for v < i≤ 2v . The matrix Ñ1 ( μ ) of the remark following Regularity Hypothesis 1 is con- sequently determined by ...
Page 2397
... Hypothesis ( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11. Hypothesis ( ii ) has been established and is given by Lemma 7 ( iv ) . It therefore only remains to establish hypothesis ( iii ) of Theorem XVIII ...
... Hypothesis ( i ) of Theorem XVIII.2.34 is satisfied by virtue of Corollaries 9 and 11. Hypothesis ( ii ) has been established and is given by Lemma 7 ( iv ) . It therefore only remains to establish hypothesis ( iii ) of Theorem XVIII ...
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