Linear Operators: Spectral operators |
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Page 2000
... sphere in RN . Then , by changing to spherical polar coordinates ( r , w ) where s = rw with r≥0 , w = 1 , we have , for 0 < ɛ < r , S__ | f ( s ) ds = - S. { S_ \ ( pc ) p * -1 } m ( du ) dp 8 = S dp M = √ 22 { | __ \ f ( w ) \ m ...
... sphere in RN . Then , by changing to spherical polar coordinates ( r , w ) where s = rw with r≥0 , w = 1 , we have , for 0 < ɛ < r , S__ | f ( s ) ds = - S. { S_ \ ( pc ) p * -1 } m ( du ) dp 8 = S dp M = √ 22 { | __ \ f ( w ) \ m ...
Page 2258
... sphere into two regions R1 and R2 , surrounding the points of R1 ( resp . , R2 ) in the positive ( resp . , the negative ) sense of complex function theory ; in what follows , we shall refer to the inter- section of R ( resp . , R2 ) ...
... sphere into two regions R1 and R2 , surrounding the points of R1 ( resp . , R2 ) in the positive ( resp . , the negative ) sense of complex function theory ; in what follows , we shall refer to the inter- section of R ( resp . , R2 ) ...
Page 2309
... sphere of L2 ( I ) , and { f } a sequence of elements of S - 1U , then f , may be written as fn = S - 1gn with gn in U. The space L2 ( 1 ) being reflexive , the sequence { g } has a weakly convergent subse- quence with weak limit g ...
... sphere of L2 ( I ) , and { f } a sequence of elements of S - 1U , then f , may be written as fn = S - 1gn with gn in U. The space L2 ( 1 ) being reflexive , the sequence { g } has a weakly convergent subse- quence with weak limit g ...
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