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 2344
... boundary conditions , of which n / 2 are boundary conditions at zero and n / 2 are boundary conditions at 1. Then all the conclusions of Theorem 8 are valid . In this connection , it is also worth making a simple remark on the notion of ...
... boundary conditions , of which n / 2 are boundary conditions at zero and n / 2 are boundary conditions at 1. Then all the conclusions of Theorem 8 are valid . In this connection , it is also worth making a simple remark on the notion of ...
Page 2350
... boundary conditions C ( Uf ) = 0 is regular ) to assume that an - 1 ( t ) = 0. But , under the condition that the set of boundary conditions C ( Uf ) = 0 is regular , this has been established above . Thus , to complete the proof , it ...
... boundary conditions C ( Uf ) = 0 is regular ) to assume that an - 1 ( t ) = 0. But , under the condition that the set of boundary conditions C ( Uf ) = 0 is regular , this has been established above . Thus , to complete the proof , it ...
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