Linear Operators: General theory |
From inside the book
Results 1-3 of 48
Page 651
... transformation f { 4 } takes the familiar " convolution " form ∞ [ f { A } x ] ( t ) = [ _ % x ( t — s ) ß ( ds ) . 81 ... transform y ( t ) = 1 π £ 18 sech ( 1-1 ) 2 x ( s ) ds provides an example for the inversion Theorem 13. In this ...
... transformation f { 4 } takes the familiar " convolution " form ∞ [ f { A } x ] ( t ) = [ _ % x ( t — s ) ß ( ds ) . 81 ... transform y ( t ) = 1 π £ 18 sech ( 1-1 ) 2 x ( s ) ds provides an example for the inversion Theorem 13. In this ...
Page 667
... transformation p ( i.e. , one for which μ ( p − 1 ( e ) ) = μ ( e ) for every e in E ) satisfies the hy- pothesis of the preceding theorem . It has been mentioned earlier that it is exactly this type of transformation which arises in ...
... transformation p ( i.e. , one for which μ ( p − 1 ( e ) ) = μ ( e ) for every e in E ) satisfies the hy- pothesis of the preceding theorem . It has been mentioned earlier that it is exactly this type of transformation which arises in ...
Page 799
... transforms . Duke Math . J. 13 , 307-330 ( 1946 ) . Pólya , G. 1 . Remark on Weyl's note “ Inequalities between the ... transform . Doklady Akad . Nauk SSSR ( N. S. ) 57 , 871-874 ( 1947 ) . ( Russian ) Math . Rev. 9 , 236 ( 1948 ) . On ...
... transforms . Duke Math . J. 13 , 307-330 ( 1946 ) . Pólya , G. 1 . Remark on Weyl's note “ Inequalities between the ... transform . Doklady Akad . Nauk SSSR ( N. S. ) 57 , 871-874 ( 1947 ) . ( Russian ) Math . Rev. 9 , 236 ( 1948 ) . On ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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