Linear Operators: Spectral operators |
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Page 2118
... regular if it has a regular spectral distribution . Although it is not known whether or not every generalized scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given any two regular spectral distributions U ...
... regular if it has a regular spectral distribution . Although it is not known whether or not every generalized scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given any two regular spectral distributions U ...
Page 2158
... regular relative to T is dense on To , then every closed subinterval of T。 whose end points are regular relative to T is in S ( T ) and every Borel subset of the plane is measurable T. 0 PROOF . Let y be a closed subinterval of To ...
... regular relative to T is dense on To , then every closed subinterval of T。 whose end points are regular relative to T is in S ( T ) and every Borel subset of the plane is measurable T. 0 PROOF . Let y be a closed subinterval of To ...
Page 2344
... regular boundary conditions in the case of a second order differential operator . If the boundary conditions are ... regular , that the boundary conditions [ * ] are regular . ( b ) m1 = 0 , m2 = 0. In this case , the boundary conditions ...
... regular boundary conditions in the case of a second order differential operator . If the boundary conditions are ... regular , that the boundary conditions [ * ] are regular . ( b ) m1 = 0 , m2 = 0. In this case , the boundary conditions ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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