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By G. N. Watson

An Unabridged, Digitally Enlarged Printing, to incorporate: The Tabulation Of Bessel features - Bibliography - Index Of Symbols - checklist Of Authors Quoted, And A accomplished Index

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A^d) is at least the value on the right-hand side of the inequality (10). ,iA1>l1,- • • , < ; / > G Qd « , • • • , < , ) be an arbitrary algorithm. For j = 1 , . . , d put Tj = T{I/4, • • • , ^ ) := sup{F,-(y) : y G F , , ^ ( y ) = 0, fc = 1,.. ,71,}, i? ,d. ,Uj, m € N and Fj (yj,m) = Tj • sgn (Pj(2TT) - Fj(0)) . (13) Denote zm (tu ... ,td) = yliTn (ti) + . . + yd,m (td), m G N. Obviously, zm G Yx + . . + Yd C Y. JE By the choice of the sequences, Vf (Vj,™,) — fQnyj,m{t)dtp{. the indexes. Then, T(zm) = 0 and d d = 0 for all values of 2n d R(Y;F,T)>\F(zm)\= 19 ]T J J' yjim (*,) dF, dFx..

Suppose a regular topological space contains an uncountable metrizable compact subset and has the strong Skorokhod property for uniformly tight weakly convergent sequences of measures with compact support. If X admits a 38 Taras Banakh et al. sequentially continuous binary operation o : X x X —> X with a sequentially continuous cancellation, then X is an a4-space. If the operation o is sequentially invertible (and the space X has countable cs*-network or is a monotone tt-space), then X is sequentially homeomorphic to a (first-countable) strong Frechet space.

Temlyakov, Approximate recovery of periodic functions of several variables, Mat. Sbornik 128 (2) (1985) 256-268 (Russian). 23. A. Zhensykbaev, Best quadrature formula for certain classes of periodic differentiable functions, Izv. Akad. Nauk SSSR, Ser. Mat. 41 (5) (1977) 11101124 (Russian). 24. A. Zhensykbayev, Monosplines of minimal norm and best quadrature formulae, Uspekhi Mat. Nauk 36 4(220) (1981) 107-159. Functional Analysis and its Applications V. Kadets and W. V. All rights reserved 23 Topological spaces with the strong Skhorokhod property, II Tar as Banakh Lviv National University, Department of Mechanics and Mathematics, Universytetska 1, 79000, Ukraine Vladimir I.

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