Linear Operators: Spectral operators |
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Page 2068
... satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo L1 L1 satisfies ( 11 ) . More generally ...
... satisfies ( 11 ) . Also the space Lo L1 C of all inte- grable functions which coincide almost everywhere with a continuous function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo L1 L1 satisfies ( 11 ) . More generally ...
Page 2112
... satisfies the condition : ( a ) N ( F1 , T ) M ( F2 , T ) , if F the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X admits ...
... satisfies the condition : ( a ) N ( F1 , T ) M ( F2 , T ) , if F the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X admits ...
Page 2314
... satisfies the boundary condition at t = 0 if tan sa = kos , and satisfies the boundary conditions at t = 1 if tan s ( 1 + x ) = k1s . Thus , using the addition formula for the tangent function , TX can only fail to have an inverse if λ ...
... satisfies the boundary condition at t = 0 if tan sa = kos , and satisfies the boundary conditions at t = 1 if tan s ( 1 + x ) = k1s . Thus , using the addition formula for the tangent function , TX can only fail to have an inverse if λ ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ 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 operator 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 subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero