Linear Operators: Spectral operators |
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Page 2307
... values for T. Let S be the unbounded operator in L2 ( I ) derived from T by imposition of the boundary conditions A ( f ) = 0 , i = 1 , ... , m . Then every ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
... values for T. Let S be the unbounded operator in L2 ( I ) derived from T by imposition of the boundary conditions A ( f ) = 0 , i = 1 , ... , m . Then every ... BOUNDARY CONDITIONS Separated Boundary Conditions for the Second Order Operator.
Page 2342
... boundary values for 7 at 0 , By + 1 , ... , B2 , being boundary values for 7 at 1. By the remark following formula ( 3 ) , it is no loss of generality to assume that the order of B , is m1 , and that m1 > m2 > > My , my +1 > Mv + 2 ...
... boundary values for 7 at 0 , By + 1 , ... , B2 , being boundary values for 7 at 1. By the remark following formula ( 3 ) , it is no loss of generality to assume that the order of B , is m1 , and that m1 > m2 > > My , my +1 > Mv + 2 ...
Page 2343
... boundary values ( 1 ) may be separated into a set of v boundary values at zero and a set of v boundary values at 1 . We state all this as a formal theorem . 14 ν THEOREM ( H. P. Kramer ) . Let n be even and let T be the closed operator ...
... boundary values ( 1 ) may be separated into a set of v boundary values at zero and a set of v boundary values at 1 . We state all this as a formal theorem . 14 ν THEOREM ( H. P. Kramer ) . Let n be even and let T be the closed operator ...
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