Linear Operators: Spectral operators |
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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 ) a A B2a a22 where ẞ0 is a complex constant , a გ α = + + αN 081 JSN and the ...
... 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 ) a A B2a a22 where ẞ0 is a complex constant , a გ α = + + αN 081 JSN and the ...
Page 2486
... consider the space L2 = L2 ( R , H ) . Let H be the self adjoint operator in L2 defined by ( Hƒ ) ( x ) = xf ( x ) . For each ❤ Є L2 , let T be the self adjoint operator with one - dimensional range defined by Tof = q ( f , q ) . Let c ...
... consider the space L2 = L2 ( R , H ) . Let H be the self adjoint operator in L2 defined by ( Hƒ ) ( x ) = xf ( x ) . For each ❤ Є L2 , let T be the self adjoint operator with one - dimensional range defined by Tof = q ( f , q ) . Let c ...
Page 2488
... Consider A self adjoint , and expand in the eigenvectors of A. ) 17 ( a ) Let f be a continuous function of bounded variation on an interval [ a , b ] , and let V ( ƒ ) denote its total variation . Show that \ [ e " J = ) dz \ = eixf ...
... Consider A self adjoint , and expand in the eigenvectors of A. ) 17 ( a ) Let f be a continuous function of bounded variation on an interval [ a , b ] , and let V ( ƒ ) denote its total variation . Show that \ [ e " J = ) dz \ = eixf ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operators Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero