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Page 505
... equation that x * ( s ) = x * ( s ) for u - almost all s in S. Equation ( ii ) holds for a and xo therefore equation ( i ) does likewise . Q.E.D. In the following theorem it is shown that if the range of an opera- tor on L1 ( S , 2 , μ ) ...
... equation that x * ( s ) = x * ( s ) for u - almost all s in S. Equation ( ii ) holds for a and xo therefore equation ( i ) does likewise . Q.E.D. In the following theorem it is shown that if the range of an opera- tor on L1 ( S , 2 , μ ) ...
Page 762
... equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On differential equations with non - oscillatory eigenfunctions . Duke Math . J. 15 , 697-709 ( 1948 ) . On the linear logarithmico - exponential differential equation of ...
... equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . On differential equations with non - oscillatory eigenfunctions . Duke Math . J. 15 , 697-709 ( 1948 ) . On the linear logarithmico - exponential differential equation of ...
Page 763
... equation . Amer . J. Math . 71 , 206-213 ( 1949 ) . On the location of spectra of wave equations . Amer . J. Math.71,214–217 ( 1949 ) . On the Laplace - Fourier transcendents . Amer . J. Math . 71 , 367–372 ( 1949 ) . 10. Oscillatory ...
... equation . Amer . J. Math . 71 , 206-213 ( 1949 ) . On the location of spectra of wave equations . Amer . J. Math.71,214–217 ( 1949 ) . On the Laplace - Fourier transcendents . Amer . J. Math . 71 , 367–372 ( 1949 ) . 10. Oscillatory ...
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