Linear Operators: General theory |
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Page 38
... transformation . Unless otherwise stated , the coefficient field for a linear space X will be either the field of real numbers , in which case X is called a real linear space , or the field of complex numbers , in which case X is called ...
... transformation . Unless otherwise stated , the coefficient field for a linear space X will be either the field of real numbers , in which case X is called a real linear space , or the field of complex numbers , in which case X is called ...
Page 651
... transformation f { 4 } takes the familiar € " convolution " form ∞ [ ƒ { A } x ] ( t ) = ƒ ‰% x ( t — s ) ß ( ds ) ... transform 1 ∞ ( t - s ) y ( t ) sech x ( s ) ds π -∞ 2 provides an example for the inversion Theorem 13. In this ...
... transformation f { 4 } takes the familiar € " convolution " form ∞ [ ƒ { A } x ] ( t ) = ƒ ‰% x ( t — s ) ß ( ds ) ... transform 1 ∞ ( t - s ) y ( t ) sech x ( s ) ds π -∞ 2 provides an example for the inversion Theorem 13. In this ...
Page 728
... transforms by differential operators of infinite order . There is an extensive literature on this problem -- particularly ... transform and { p , ( D ) } is an inverting sequence . References to further discussions of this problem may be ...
... transforms by differential operators of infinite order . There is an extensive literature on this problem -- particularly ... transform and { p , ( D ) } is an inverting sequence . References to further discussions of this problem may be ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ