Linear Operators: General theory |
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Page 227
... formula : f ( z ) = 1 S f ( x ) ΣπίJaz 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 ( z ) = 1 S f ( x ) ΣπίJaz 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 ] F ( x , t ) = at 1 2 4 0x2 F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; F ( x , 0 ) = f ( x ) , V being a given coefficient function . This ...
... formula for the solution . F of the more general parabolic initial value problem . a [ 1 ] F ( x , t ) = at 1 2 4 0x2 F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; F ( x , 0 ) = f ( x ) , V being a given coefficient function . This ...
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