Linear Operators: Spectral operators |
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Page 2017
... formal differ- ential operator : ( 15 ) 22 2 i 781 782 a2 as 2 1 22 Əs2 0 Here we have S1 = RN and S2 is void , so that inequality ( i ) of Theorem 6 is satisfied but equation ( ii ) is not . Thus the natural closed extension A of the ...
... formal differ- ential operator : ( 15 ) 22 2 i 781 782 a2 as 2 1 22 Əs2 0 Here we have S1 = RN and S2 is void , so that inequality ( i ) of Theorem 6 is satisfied but equation ( ii ) is not . Thus the natural closed extension A of the ...
Page 2305
... formal differential operator d ( 1 — t2 ) dt d 2α2 282 + + dt 1 + t 1 of the first part of Section XIII.8 , and again make the assumption made there that a , B. Then by the theory of Chapter XIII ( compare the discussion in Section XIII ...
... formal differential operator d ( 1 — t2 ) dt d 2α2 282 + + dt 1 + t 1 of the first part of Section XIII.8 , and again make the assumption made there that a , B. Then by the theory of Chapter XIII ( compare the discussion in Section XIII ...
Page 2371
... formal differential operator . The abstract operator - theoretic approach via perturbation theorems used in Section 2 was introduced by J. Schwartz [ 2 ] , and extended by H. P. Kramer [ 2 ] to the general case . Some results similar to ...
... formal differential operator . The abstract operator - theoretic approach via perturbation theorems used in Section 2 was introduced by J. Schwartz [ 2 ] , and extended by H. P. Kramer [ 2 ] to the general case . Some results similar to ...
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