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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 ...
... 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 ...
Page 762
... equations in Hilbert spaces . Soobščeniya Akad . Nauk Gruzin . SSR 13 , 65-72 ( 1952 ) . ( Russian ) Math . Rev. 14 ... equation . Amer . J. Math . 71 , 915-920 ( 1949 ) . The number of L - solutions of x " + q ( t ) x 0. Amer . J. Math ...
... equations in Hilbert spaces . Soobščeniya Akad . Nauk Gruzin . SSR 13 , 65-72 ( 1952 ) . ( Russian ) Math . Rev. 14 ... equation . Amer . J. Math . 71 , 915-920 ( 1949 ) . The number of L - solutions of x " + q ( t ) x 0. Amer . J. Math ...
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 ...
... 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 ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ