Linear Operators: Spectral operators |
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Page 1998
... examples are among the most familiar convolutions in A. EXAMPLE ( Translation ) . Let λ ( o ) = 1 if t is in σ ; otherwise let λ ( o ) = 0 . Then ( λ ; * q ) ( s ) = q ( s − t ) . Then - 12 EXAMPLE ( Convolution by an L1 function ) ...
... examples are among the most familiar convolutions in A. EXAMPLE ( Translation ) . Let λ ( o ) = 1 if t is in σ ; otherwise let λ ( o ) = 0 . Then ( λ ; * q ) ( s ) = q ( s − t ) . Then - 12 EXAMPLE ( Convolution by an L1 function ) ...
Page 1999
... example shows that ƒ * q = q * f = [ _p ( s ) e ( ds ) f = S 7 ( ƒ * q ) = { _p ( s ) re ( ds ) ƒ = [ _p ( s ) μ ( ds ) } = } ÿ = { } ( 8 ) μ ( ds ) ğ ƒ * q = [ _ } ( s ) e ( ds ) q . G By using a sequence { n } in L1 L2 to approach an ...
... example shows that ƒ * q = q * f = [ _p ( s ) e ( ds ) f = S 7 ( ƒ * q ) = { _p ( s ) re ( ds ) ƒ = [ _p ( s ) μ ( ds ) } = } ÿ = { } ( 8 ) μ ( ds ) ğ ƒ * q = [ _ } ( s ) e ( ds ) q . G By using a sequence { n } in L1 L2 to approach an ...
Page 2020
... example , with p = 2 , is the perturbed Laplacian ( 19 ) A = ( V2 02 ǝ2 V2 - V2 , + + Əs2 and a = Here ( 20 ) a ( 0 ... example which has features not seen in the preceding examples is given by the formal differential operator ( 21 ) a a ...
... example , with p = 2 , is the perturbed Laplacian ( 19 ) A = ( V2 02 ǝ2 V2 - V2 , + + Əs2 and a = Here ( 20 ) a ( 0 ... example which has features not seen in the preceding examples is given by the formal differential operator ( 21 ) a a ...
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