On the distribution of points of maximal deviation in complex Čebyšev approximation

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On the distribution of points of maximal deviation in complex ebyev approximation

     

Converse results on equiconvergence of interpolating polynomials

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On unconditionally convergent basis expansions in the space of continuous functions

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This paper was written during the author's scholarship at the State University of Odessa in the USSR.     

On a test of Jordan type for double Fourier series with respect to multiplicative systems

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On Szalay's theorem of double series

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Maximal inequalities,convexity inequality,and their duality. II

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On the admissibility of function spaces of typeB p,q s andF p,q s,and boundary value problems for non-linear partial differential equations

u=f(x)+S(u), S — , u-G(u), G — . B _p,q ^s () -F _p,q ^s (). R _n — . — . _p,q ^s F _p,q ^s .     

Langlands classification for real Lie groups with reductive Lie algebra

LetG be a (not necessarily connected) real Lie group with reductive Lie algebra. We consider representations ofG which some call admissible but we call them of Harish-Chandra type. We show that any nontempered irreducible Harish-Chandra type representation ofG is infinitesimally equivalent to the Langlands quotient obtained from an essentially unique triple (M, V, ) of Langlands data; while for tempered irreducible Harish-Chandra type representations we prove they are infinitesimally subrepresentations of some induced representations U^V, with imaginary and withV from the quasi-discrete series of a suitableM (perhapsG=M; we define the quasi-discrete series in Definition 4.5 of this paper.We show that irreducible continuous unitary representations of really reductive groups are of Harish-Chandra type. Then the results above yield the canonical decomposition of the unitary spectrum>G for any really reductiveG. In particular, this holds ifG/G ₀ is finite, so the center of the connected semi-simple subgroup with Lie algebra [g, g] may be infinite!Research supported, in part, by the Hungarian National Fund for Scientific Research (grant Nos. 1900 and 2648).     

On the dimensions of automorphism groups of eight-dimensional ternary fields,II

LetT be an eight-dimensional, connected, locally compact ternary field and let denote a connected closed Lie subgroup of its automorphism group which is taken with the compact-open topology. It is proved that if the ternary fixed fieldF of is connected, then is either isomorphic to one of the compact Lie groupsG ₂ or SU₃, or the (covering) dimension of is at most 7.     

A local comparison theorem with applications to approximation in certain group and multiplier algebras

X- E — -. , X . . Rⁿ Rⁿ/(2Z)ⁿ L ^p(Rⁿ) . -R _t f , (-1)/2.

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The contribution of the first author was supported in part by Grant No. II B 7 — FA 5334 awarded by the Minister für Wissenschaft und Forschung des Landes Nordrhein-Westfalen.     

Fundamental equation of information revisited

Summary This paper presents a new, shorter and more direct proof of the following result of J. Aczél and C. T. Ng: IfM: J R (J =]0, 1[ ^k ) is both multiplicative and additive, then the general solution: J R of(x) + M(1 – x)(y/1 – x) = (y) + M(1 – y)(x/1 – y) (x, y, x + y J) is given by(x) = ifM = 0,(x) = M(x)[L(x) + ] + M(1 – x)L(1 – x) ifM 0,where is an arbitrary constant andL: J R is an arbitrary solution of the logarithmic functional equationL(xy) = L(x) + L(y) (x, y J). Also, some extensions of this result to fields more general than the reals are given.     

Atomic Hardy spaces

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This paper is a part of the author's Ph.D. thesis written under the supervision of Prof. F. Schipp, Eötvös L. University, Budapest.     

On the optimality of a characterization theorem for the gamma function using the multiplication formula

Summary The following Artin type characterization of : _{+ +} is proved: Assume thatf: _{+ +} satisfies the Gauss multiplication formula for some fixedp 2,f is absolutely continuous on [l/p, 1 + ] for some > 0 and lim _{x 0} xf(x) = 1. Thenf(x) = (x) forx > 0.The optimality of this result is checked by means of counterexamples. For instance, it is shown that the result is no longer true, if f is absolutely continuous is replaced by f is continuous and of finite variation.     

Generalized localization and convergence tests for double trigonometric Fourier series of functions fromL p,p>1

. E , f(x)L _p (T ^N ),P1,f(x)=0 E (E— ^N =[-, ]^N) E , . , .

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In closing the author thanks V. A. Il'in and . A. Alimov for their constant attention paid to the present work.     

A Remark on Real Parameter Global Bifurcation

We study the nonlinear eigenvalue problem F(x,) = L()x +R(x,) = 0 where F : X × R X with X a Hilbert space. IfL() is a polynomial in , then it is shown that 0> 0 is a global bifurcation point of the eigenvalue problem provided astandard transversality condition is satisfied, the dimension of the nullspace of L(0) is an odd number and L() is composed of asequence of positive operators on the finite dimensional null space ofL(0).     

Transferring estimates for zonal convolution operators

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WT measure vector spaces

n- M WT- , M n–1 . . WT- . .     

Designs and partial geometries over finite fields

Let be a finite field, and let (, B) be a nontrivial 2-(n, k, 1)-design over . Then each point induces a (k–1)-spread S on /. (, B) is said to be a geometric design if S is a geometric spread on / for each . In this paper, we prove that there are no geometric designs over any finite field .Research partially supported by NSF grant DMS-8703229.     

Some remarks on the approximation in the strong sense

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On the 70th birthday of Professor S. M. Nikol'skii     

О решеткахИ-Радикалов, строгих слева Радикалов, наследственных слева радикалов

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