Linear Operators: General theory |
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Page 227
... formula : 1 f ( a ) f ( z ) = 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 : 1 f ( a ) f ( z ) = 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 . д [ † ] F ( x , t ) - Ət 1 მ 2 4 dx2 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 . д [ † ] F ( x , t ) - Ət 1 მ 2 4 dx2 F ( x , t ) + V ( x , t ) F ( x , t ) , t≥ 0 ; F ( x , 0 ) = f ( x ) , V being a given coefficient function . This ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ