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Page 651
... transformation ƒ { 4 } takes the familiar " convolution " form A = ∞ [ 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 ƒ { 4 } takes the familiar " convolution " form A = ∞ [ 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 ...
Page 822
... transforms . Duke Math . J. 14 , 217-249 ( 1947 ) . 3. The convolution transform . Bull . Amer . Math . Soc . 60 , 444-456 ( 1954 ) . Widder , D. V. , and Hirschman , I. I. 1. The inversion of a general class of convolution transforms ...
... transforms . Duke Math . J. 14 , 217-249 ( 1947 ) . 3. The convolution transform . Bull . Amer . Math . Soc . 60 , 444-456 ( 1954 ) . Widder , D. V. , and Hirschman , I. I. 1. The inversion of a general class of convolution transforms ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ