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November 2, 2016
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December 31, 1967
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03 at A. 1. On.the akebrafe number of cloied extranuds an A Mathematical Review a Id Doklady Akad. Ngkuk SSSR (N.S.).,, 89, " I& W2_1 I S .Vol. 14 No. 10 61 1 3). (Russian) , " I ~ I :. , - '. 11 11. Nov. 1953 Let R be a closed manifold whose t'n v- I first Betti gir mpg Analysis (mod-2) vanish and whose mth Betti .gioup contains at least one element of even order. The author's main result 1,o/ is that, given any positive regulai'variational problem for curves on R, the algebraic nui bar of.closed extremils is m not less than 3; and further that there exist'. either con.' tinuum-many closed extremals of equal length, or else 3 closed extremal~ of indices w -~ 1, 2 (m ~- 1). 3 (m -;, 1),~ This generalixes, an earlier result In which R was'assumed to be a 2-sphere [same Doklady (N.S.) 66; 3j7-3SO (1949); these Rev. 11, 4.7]. The tools needed for this ektinsion Include a lower es jimate of dje "length" (mod 2), in the sense of FroIoffl´┐Żnd.E!WI Mat. Sbornlk 42, 63~:192 (1935)11 of tFe space of!~Iosed non-oriented curyea on R. is "length", and also the Uwternlk-Schnlmlma~n catEjor~, am' showo to be not less than 3.' L. a Younj ~( ladisoo, Wi4j, A. 1. 'A Author. i : A~ Ij: Genersuistio~ f; t ~I;im -Theorem on the, he Undk4hnirellman" , f other the-orwa connected with icovisr n o s -fieres of some the fomer* Perlodical Doki 'AN -S= :95 M9 n 51 21 Apr 1954 Ostract t The the Lusternik-Shnirellman theorem on the covering of spheres Where-this reflection condition* in'respect~-to the centerap Is:changiod into an-arbitrary conaition for involute reflection of,sphares upon themaelves, Some other theorem related to. this one just mentioned-are also considered. V. A. .8teklovV I*th. Institute of the Acad, of Scs. of the USSR fiSubadtted ~5~ fob 1954 T- Call Nr: AF 1108825 Transactions of the Third All-union Mathematical Congress (Cont. )mo86ow., Jun-Jul '56, Trudy '56, v. 1, Seat. Rpts., Izdatel'stvo AN SSSR, Moscow, 1956, 237 PP. There are 11 references, all of them USSR. TAkhtenbawn, L. M..(Mosoow), Characteristic Nwnbers of Improper Graph. :135-136 Smirnov, Yu.,M. (Moscow). On the Extension of Topological Spaces. 136 Smirnov, Yu. M. (Moscow). On Metrisation of Local Compact Spaces Which are Decomposable into the Sum of Countable Number of Sets With Countable Bases. 136-137 Mention is made of Aleksandrov, P. S. and Uryson, P. S. Eet A. I. (Novosibirsk). Calculus of Variations in the LFLX;g- e 137 Mention is made of Lyusternik, L. A., Shnirellman, Shvarts., A. S., Allber, S. I# and Pontryagin, L. S. Card 44/80 4L ..-Al4h _;M .M -1 WNR-v M E .~ a SUBJECT 'USSR/MATHMTICS/Functional analysis CARD 1/2 PG - 475 AUTHOR FET A.I. TITLE VnW a-pace of analytic functions and its application to the Cauchy~Kowalevski problem* PERIODICAL Uspechi mat.Rauk 11.2 21 215-222 (1956) reviewed 1/1957 The author shows that the class A of functions being uniformly convergent in the unit circle, can be changed in a K-space (nee Kaztorovig "functional analysis") such that a corresponding convergence inside of the unit circle is identical with the uniform convergence. This permits the application of general function-theoretioal schemes for the theorem of S.Kowalevski too, The author proves that the problem ui I n (k) u N 9t - z r ij + F_ b ij'j + 01 J-1 k-1 -~Xk J-1 Uj(Otxl,-.g,txn) - 0 (1-19 ... IN) (akj, bijpci are analytic functions of the real variable i tIx1I---xn in Itl