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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero