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Page 642
... transform of ß . We denote by ( 4 ) the family of bilateral Laplace transforms of measure ẞe S ( A ) . If ẞ in ( 4 ) is continuous with respect to Lebesgue - Stieltjes meas- ure and if F is the function in L1 ( -∞ , ∞ ) given by the ...
... transform of ß . We denote by ( 4 ) the family of bilateral Laplace transforms of measure ẞe S ( A ) . If ẞ in ( 4 ) is continuous with respect to Lebesgue - Stieltjes meas- ure and if F is the function in L1 ( -∞ , ∞ ) given by the ...
Page 651
... transformation ƒ { A } takes the familiar " convolution " form [ f { A } x ] ( t ) = √∞∞ x ( t — s ) ẞ ( ds ) . In ... transform 1 ( t - 8 ) y ( t ) sech x ( s ) ds 2 provides an example for the inversion Theorem 13. In this VIII.2.14 ...
... transformation ƒ { A } takes the familiar " convolution " form [ f { A } x ] ( t ) = √∞∞ x ( t — s ) ẞ ( ds ) . In ... transform 1 ( t - 8 ) y ( t ) sech x ( s ) ds 2 provides an example for the inversion Theorem 13. In this VIII.2.14 ...
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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ