Decomposition numbers modulo p of certain representations of the groups
A. Zalesskii (1990)
Banach Center Publications
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A. Zalesskii (1990)
Banach Center Publications
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Stanisław Bylka, Jan Komar (2007)
Discussiones Mathematicae Graph Theory
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This paper deals with weighted set systems (V,,q), where V is a set of indices, and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family of subsets of a set S such that for each E ∈ . A necessary condition...
Camillo Trapani, Salvatore Triolo (2008)
Studia Mathematica
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Representations of a module over a *-algebra are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of .
Michael Lacey (2011)
Banach Center Publications
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For an L²-bounded Calderón-Zygmund Operator T acting on , and a weight w ∈ A₂, the norm of T on L²(w) is dominated by . The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973 (MR0312139), has been established in different levels of generality by a number of authors over the last few years. It has a subtle proof, whose full implications will unfold over the next few years. This sharp estimate requires that the A₂ character of the weight can...
Zhi-Hong Sun (2008)
Acta Arithmetica
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Wojciech M. Zajączkowski (2009)
Applicationes Mathematicae
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The existence of solutions to the elliptic problem rot v = w, div v = 0 in Ω ⊂ ℝ³, , S = ∂Ω, in weighted Hilbert spaces is proved. It is assumed that Ω contains an axis L and the weight is a negative power of the distance to the axis. The main part of the proof is devoted to examining solutions in a neighbourhood of L. Their existence in Ω follows by regularization.
Michał Barski (2012)
Applicationes Mathematicae
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The risk minimizing problem in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for l(x) = x and , with p > 1 for digital, quantos, outperformance and spread options are derived.
Hidenori Katsurada, Hisa-aki Kawamura (2014)
Acta Arithmetica
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Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let be the first Fourier-Jacobi coefficient of Iₙ(h), and be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to...
S. Petermichl, J. Wittwer (2008)
Studia Mathematica
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We establish sufficient conditions on the two weights w and v so that the Beurling-Ahlfors transform acts continuously from to L²(v). Our conditions are simple estimates involving heat extensions and Green’s potentials of the weights.
Armin Rainer, Gerhard Schindl (2014)
Studia Mathematica
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We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space and the Roumieu space as intersection and union of spaces and for associated weight sequences, respectively.
Florian Luca, Augustine O. Munagi (2014)
Colloquium Mathematicae
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We note that every positive integer N has a representation as a sum of distinct members of the sequence , where d(m) is the number of divisors of m. When N is a member of a binary recurrence satisfying some mild technical conditions, we show that the number of such summands tends to infinity with n at a rate of at least c₁logn/loglogn for some positive constant c₁. We also compute all the Fibonacci numbers of the form d(m!) and d(m₁!) + d(m₂)! for some positive integers m,m₁,m₂. ...
Wojciech M. Zajączkowski (2010)
Applicationes Mathematicae
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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, , S = ∂Ω in weighted -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.
Ernest X. W. Xia (2014)
Colloquium Mathematicae
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For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form . Lomadze discovered a formula for R(6,0;n). Explicit formulas for R(1,5;n), R(2,4;n), R(3,3;n), R(4,2;n) and R(5,1;n) are determined in this paper by using the (p;k)-parametrization of theta functions due to Alaca, Alaca and Williams.
Dorothee D. Haroske (2011)
Banach Center Publications
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We study continuity envelopes of function spaces and where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
J. de Vries (1978)
Colloquium Mathematicae
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Paul Balmer (2015)
Journal of the European Mathematical Society
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We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group , the derived and the stable categories of representations of a subgroup can be constructed out of the corresponding category for by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods...
David Cruz-Uribe, SFO (2001)
Studia Mathematica
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We prove two-weight norm inequalities in ℝⁿ for the minimal operator , extending to higher dimensions results obtained by Cruz-Uribe, Neugebauer and Olesen [8] on the real line. As an application we extend to ℝⁿ weighted norm inequalities for the geometric maximal operator , proved by Yin and Muckenhoupt [27]. We also give norm inequalities for the centered minimal operator, study powers of doubling weights and give sufficient conditions for the geometric maximal operator to be equal...
William D. Banks, Igor E. Shparlinski (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We study values of the Euler function φ(n) taken on binary palindromes of even length. In particular, if denotes the set of binary palindromes with precisely 2ℓ binary digits, we derive an asymptotic formula for the average value of the Euler function on .
Yen Do, Michael Lacey (2012)
Studia Mathematica
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For 1 < p < ∞ and for weight w in , we show that the r-variation of the Fourier sums of any function f in is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational...
Filip Soudský (2016)
Commentationes Mathematicae Universitatis Carolinae
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We give a full characterization of normability of Lorentz spaces . This result is in fact known since it can be derived from Kamińska A., Maligranda L., On Lorentz spaces, Israel J. Funct. Anal. 140 (2004), 285–318. In this paper we present an alternative and more direct proof.
S. J. Bhatt, P. A. Dabhi, H. V. Dedania (2009)
Studia Mathematica
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Let 0 < p ≤ 1, let ω: ℤ → [1,∞) be a weight on ℤ and let f be a nowhere vanishing continuous function on the unit circle Γ whose Fourier series satisfies . Then there exists a weight ν on ℤ such that . Further, ν is non-constant if and only if ω is non-constant; and ν = ω if ω is non-quasianalytic. This includes the classical Wiener theorem (p = 1, ω = 1), Domar theorem (p = 1, ω is non-quasianalytic), Żelazko theorem (ω = 1) and a recent result of Bhatt and Dedania (p = 1). An...
Gerald W. Schwarz (1987)
Annales de l'institut Fourier
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Let be a reductive complex algebraic group, and let denote the algebra of invariant polynomial functions on the direct sum of copies of the representations space of . There is a smallest integer such that generators and relations of can be obtained from those of by polarization and restitution for all . We bound and the degrees of generators and relations of , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics. ...