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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator 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 operators 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 sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero