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Page 469
... integral I ( t ) = f . . . √ Do ( t ; x ) dx1 . . . din • ... It is clear ... integral sign and employ [ * ] to conclude that I ' ( t ) is a sum of integrals ... square root { 1- ( a + ... + æ ; _ ? + æ ; + 22 + . . . + a ) } 1/2 , and a ...
... integral I ( t ) = f . . . √ Do ( t ; x ) dx1 . . . din • ... It is clear ... integral sign and employ [ * ] to conclude that I ' ( t ) is a sum of integrals ... square root { 1- ( a + ... + æ ; _ ? + æ ; + 22 + . . . + a ) } 1/2 , and a ...
Page 781
... integrable square of the system of differential equations . —y ' ' + P ( t ) y = λy . Doklady Akad . Nauk SSSR ( N.S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1. On the theory of regular ...
... integrable square of the system of differential equations . —y ' ' + P ( t ) y = λy . Doklady Akad . Nauk SSSR ( N.S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1. On the theory of regular ...
Page 807
... integrable square . J. London Math . Soc . 24 , 207-215 ( 1949 ) . Note on the uniqueness of Green's functions associated with certain differential equations . Canadian J. Math . 2 , 314–325 ( 1950 ) . On the spectrum of a certain ...
... integrable square . J. London Math . Soc . 24 , 207-215 ( 1949 ) . Note on the uniqueness of Green's functions associated with certain differential equations . Canadian J. Math . 2 , 314–325 ( 1950 ) . On the spectrum of a certain ...
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