Linear Operators: General theory |
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Page 227
... formula : f ( x ) = 1 f ( x ) 2πίδα- -z da , where z is a point of the bounded open set U whose boundary B con- sists of a finite number of closed rectifiable Jordan curves oriented in the positive sense customary in complex variable ...
... formula : f ( x ) = 1 f ( x ) 2πίδα- -z da , where z is a point of the bounded open set U whose boundary B con- sists of a finite number of closed rectifiable Jordan curves oriented in the positive sense customary in complex variable ...
Page 228
... formula in several variables , the following convergence theorem of Weierstrass : Let fn be a uniformly bounded sequence of vector valued functions each defined and analytic on an open set U in the space of the complex variables 21 ...
... formula in several variables , the following convergence theorem of Weierstrass : Let fn be a uniformly bounded sequence of vector valued functions each defined and analytic on an open set U in the space of the complex variables 21 ...
Page 407
... formula for the solution F of the more general parabolic initial value problem . a 1 22 [ t ] F ( x , t ) = F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; ді 4 dx2 F ( x , 0 ) = f ( x ) , V being a given coefficient function . This formula ...
... formula for the solution F of the more general parabolic initial value problem . a 1 22 [ t ] F ( x , t ) = F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; ді 4 dx2 F ( x , 0 ) = f ( x ) , V being a given coefficient function . This formula ...
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