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Page 642
... transform of F. We now prove certain basic facts concerning Laplace - Stieltjes transforms . 00 2 LEMMA . If f is in V ( A ) , and f ( 2 ) = √∞ e - 1t ẞ ( dt ) , then fis analytic in a strip ( w + d ) < R ( 2 ) < ( w + d ) . The ...
... transform of F. We now prove certain basic facts concerning Laplace - Stieltjes transforms . 00 2 LEMMA . If f is in V ( A ) , and f ( 2 ) = √∞ e - 1t ẞ ( dt ) , then fis analytic in a strip ( w + d ) < R ( 2 ) < ( w + d ) . The ...
Page 651
... transformation f { 4 } takes the familiar A = " convolution " form = [ f { A } x ] ( t ) = √∞ % x ( t — s ) ß ( ds ) ... transform 1 ( t - s ) y ( t ) = sech x ( s ) ds πυ 2 provides an example for the inversion Theorem 13. In this VIII ...
... transformation f { 4 } takes the familiar A = " convolution " form = [ f { A } x ] ( t ) = √∞ % x ( t — s ) ß ( ds ) ... transform 1 ( t - s ) y ( t ) = sech x ( s ) ds πυ 2 provides an example for the inversion Theorem 13. In this VIII ...
Page 799
... transforms . Duke Math . J. 13 , 307-330 ( 1946 ) . Pólya , G. 1 . Remark on Weyl's note " Inequalities between the ... transform . Doklady Akad . Nauk SSSR ( N. S. ) 57 , 871–874 ( 1947 ) . ( Russian ) Math . Rev. 9 , 236 ( 1948 ) . On ...
... transforms . Duke Math . J. 13 , 307-330 ( 1946 ) . Pólya , G. 1 . Remark on Weyl's note " Inequalities between the ... transform . Doklady Akad . Nauk SSSR ( N. S. ) 57 , 871–874 ( 1947 ) . ( Russian ) Math . Rev. 9 , 236 ( 1948 ) . On ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ