Linear Operators: Spectral operators |
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Page 2327
... linearly independent solutions 91 , 92 of the equation 79 = λop such that B1 ( 91 ) = оф B1 ( 92 ) = 0 , i = 1 , ... , k . Then 1 may be represented uniquely as 91 = P1 = Σ } = 1 € 1,0 , ( μ ( ^ ) ) and , similarly , P2 = Σ } = 1 € 2 ...
... linearly independent solutions 91 , 92 of the equation 79 = λop such that B1 ( 91 ) = оф B1 ( 92 ) = 0 , i = 1 , ... , k . Then 1 may be represented uniquely as 91 = P1 = Σ } = 1 € 1,0 , ( μ ( ^ ) ) and , similarly , P2 = Σ } = 1 € 2 ...
Page 2345
... linearly independent boundary conditions for the second order operator is irregular if and only if it has one of the ... linear mapping of L2 ( 0 , 1 ) into H ( k ) ( 0 , 1 ) . - PROOF . First note that , by the first paragraph of the ...
... linearly independent boundary conditions for the second order operator is irregular if and only if it has one of the ... linear mapping of L2 ( 0 , 1 ) into H ( k ) ( 0 , 1 ) . - PROOF . First note that , by the first paragraph of the ...
Page 2394
... linearly independent , we must have a linear relation σ2 = aô1 + bơ1 . It is clear from Lemma 1 that such a linear combination can only have the indicated asymptotic form if a = 1 , b = c ( μ ( λ ) ) . Hence σ2 ( t , μ ( \ ) ) = σ1 ( t ...
... linearly independent , we must have a linear relation σ2 = aô1 + bơ1 . It is clear from Lemma 1 that such a linear combination can only have the indicated asymptotic form if a = 1 , b = c ( μ ( λ ) ) . Hence σ2 ( t , μ ( \ ) ) = σ1 ( t ...
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