Linear Operators: Spectral operators |
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Page 2307
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
... boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
Page 2320
... boundary conditions at the outset . Suppose that if B is a boundary value , we agree to call the order of the highest derivative at 0 which appears with a non - zero coefficient in the unique expression of B in the form Bƒ = Σ ...
... boundary conditions at the outset . Suppose that if B is a boundary value , we agree to call the order of the highest derivative at 0 which appears with a non - zero coefficient in the unique expression of B in the form Bƒ = Σ ...
Page 2345
... boundary conditions is regular if and only if k + k ' # 0 . Thus a set of two linearly independent boundary conditions for the second order operator is irregular if and only if it has one of the forms or u ' ( 0 ) + ku ' ( 1 ) + ··· = 0 ...
... boundary conditions is regular if and only if k + k ' # 0 . Thus a set of two linearly independent boundary conditions for the second order operator is irregular if and only if it has one of the forms or u ' ( 0 ) + ku ' ( 1 ) + ··· = 0 ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero