Linear Operators: Spectral operators |
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Page 2351
... If M is a subset of a Banach space Y , its annihilator M is the closed subspace of * defined by Mi - { y * € Y * | y * ( M ) = 0 } . The graph of a transformation T in the B - XIX.5.1 2351 APPROXIMATION BY GENERALIZED EIGENFUNCTIONS.
... If M is a subset of a Banach space Y , its annihilator M is the closed subspace of * defined by Mi - { y * € Y * | y * ( M ) = 0 } . The graph of a transformation T in the B - XIX.5.1 2351 APPROXIMATION BY GENERALIZED EIGENFUNCTIONS.
Page 2374
... EIGENFUNCTION EXPANSIONS . The question of the expansion of a given function in terms of eigenfunctions ( or generalized eigenfunctions ) of an operator has been discussed by many authors . In addition , it is desirable to know when the ...
... EIGENFUNCTION EXPANSIONS . The question of the expansion of a given function in terms of eigenfunctions ( or generalized eigenfunctions ) of an operator has been discussed by many authors . In addition , it is desirable to know when the ...
Page 2538
... eigenfunctions for the exterior problem connected with -4 . Arch . Rat . Mech . Anal . 19 , 71-73 ( 1965 ) . 4 . On the eigenfunction expansion connected with the exterior problem for the Schrödinger equation . Japanese J. Math . 36 ...
... eigenfunctions for the exterior problem connected with -4 . Arch . Rat . Mech . Anal . 19 , 71-73 ( 1965 ) . 4 . On the eigenfunction expansion connected with the exterior problem for the Schrödinger equation . Japanese J. Math . 36 ...
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