Linear Operators: Spectral operators |
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Page 2322
... hypothesis . Π1 1 REGULARITY HYPOTHESIS FOR EVEN ORDER CASE . The polynomials and π2 are of order p . If Regularity Hypothesis 1 is satisfied , we may write 2322 XIX.4.1 XIX . PERTURBATIONS OF SPECTRAL OPERATORS.
... hypothesis . Π1 1 REGULARITY HYPOTHESIS FOR EVEN ORDER CASE . The polynomials and π2 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 adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero