Linear Operators: Spectral operators |
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Page 1918
... consider as an axiomatic basis for quantum theory . ) It may also be mentioned that the Kato - Kuroda theory yields some of the most precise results available for the spectral analysis of partial differential operators . For the ...
... consider as an axiomatic basis for quantum theory . ) It may also be mentioned that the Kato - Kuroda theory yields some of the most precise results available for the spectral analysis of partial differential operators . For the ...
Page 2051
... consider a different type of perturbed Laplacian with p = 2 , N arbitrary , and given by the formal differential operator defined on Ø2 by the matrix ( 112 ) a22 a A B2a a272 where ẞ0 is a complex constant , a a a = αo + α1 + + αN JSN ...
... consider a different type of perturbed Laplacian with p = 2 , N arbitrary , and given by the formal differential operator defined on Ø2 by the matrix ( 112 ) a22 a A B2a a272 where ẞ0 is a complex constant , a a a = αo + α1 + + αN JSN ...
Page 2409
... considering the space L2 ( D ) as above , we may consider the space L , ( D , X ) of all X - valued Borel - Lebesgue measurable functions defined in D and satisfying ( 33 ) dx 1 / p { S , IF ( x , y ) " de dy ) } - { S , IS ( 2 ) dx dy } ...
... considering the space L2 ( D ) as above , we may consider the space L , ( D , X ) of all X - valued Borel - Lebesgue measurable functions defined in D and satisfying ( 33 ) dx 1 / p { S , IF ( x , y ) " de dy ) } - { S , IS ( 2 ) dx dy } ...
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