Linear Operators: General theory |
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Page 227
... formula : [ f ( x ) = 1 f ( a ) 2πίJa - 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 ( a ) 2πίJa - 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 Z1 ...
... 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 Z1 ...
Page 407
... formula for the solution F of the more general parabolic initial value problem . д 1 22 [ t ] F ( x , t ) - F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; де 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 . д 1 22 [ t ] F ( x , t ) - F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; де 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 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