A class of -sets
David Grow (1987)
Colloquium Mathematicae
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David Grow (1987)
Colloquium Mathematicae
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Matthew Daws (2011)
Studia Mathematica
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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say . In this paper, we investigate properties of . We present a short proof that can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...
Katusi Fukuyama (2001)
Colloquium Mathematicae
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By the method of Rio [10], for a locally square integrable periodic function f, we prove for almost every x and t > 0.
H. S. Mustafayev (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let A be a complex, commutative Banach algebra and let be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space is scattered (i.e., has no nonempty perfect subset). (b) Weakly almost periodic...
Yongxiang Li, He Yang (2011)
Annales Polonici Mathematici
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The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation , where is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].
Andrzej Krupa (2003)
Studia Mathematica
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We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on . The support of the density coincides with the spectrum of the operator in .
Shangquan Bu (2013)
Studia Mathematica
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Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces , periodic Besov spaces and periodic Triebel-Lizorkin spaces , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M)....
Weidong Gao, Yuanlin Li, Pingping Zhao, Jujuan Zhuang (2016)
Colloquium Mathematicae
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Let G be an additive finite abelian group. For every positive integer ℓ, let be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine for certain finite groups, including cyclic groups, the groups and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum...
Viktor Harangi (2011)
Fundamenta Mathematicae
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Let be arbitrary nonzero real numbers. An -decomposition of a function f:ℝ → ℝ is a sum where is an -periodic function. Such a decomposition is not unique because there are several solutions of the equation with -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the -decomposition is essentially unique. We characterize those periods for which essential...
Robert Krawczyk (2014)
Banach Center Publications
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In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.
Yongkun Li, Changzhao Li, Juan Zhang (2010)
Annales Polonici Mathematici
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By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), , j ∈ ℤ, ⎨ ⎩, where is a nonsingular matrix with continuous real-valued entries.
Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)
Commentationes Mathematicae Universitatis Carolinae
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The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for , , , and to show that this sum of mappings fits into the framework of a modification of...
Alejandro Illanes (2006)
Colloquium Mathematicae
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For a metric continuum X, let C(X) (resp., ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and be the induced functions given by and . In this paper, we prove that: • If is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1]...
Saak S. Gabriyelyan (2013)
Fundamenta Mathematicae
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Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group is a dense -closed subgroup of the compact group , where is the group G with...
Lars Omlor, Michael Leinert (2010)
Banach Center Publications
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If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant such that for every continuous positive definite g≥0, where is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at...
Lukas Spiegelhofer (2014)
Acta Arithmetica
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Integer sequences of the form , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference , which measures the deviation of the mean value of φ on the subsequence from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by attains both of its values with...
W. R. Utz (1971)
Annales Polonici Mathematici
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W. D. Gao, R. Thangadurai (2003)
Colloquium Mathematicae
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We study the structure of longest sequences in which have no zero-sum subsequence of length n (or less). We prove, among other results, that for and d arbitrary, or and d = 3, every sequence of c(n,d)(n-1) elements in which has no zero-sum subsequence of length n consists of c(n,d) distinct elements each appearing n-1 times, where and .
Lingbin Kong, Daqing Jiang (1998)
Annales Polonici Mathematici
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The fourth order periodic boundary value problem , 0 < t < 2π, with , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of .
Simon Lücking (2014)
Colloquium Mathematicae
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Let G be a metrizable, compact abelian group and let Λ be a subset of its dual group Ĝ. We show that has the almost Daugavet property if and only if Λ is an infinite set, and that has the almost Daugavet property if and only if Λ is not a Λ(1) set.
Anne-Laure Dalibard (2011)
Journal of the European Mathematical Society
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This article investigates the long-time behaviour of parabolic scalar conservation laws of the type , where and the flux is periodic in . More specifically, we consider the case when the initial data is an disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in norm like a self-similar profile for large times. The proof uses a time and space change of variables...
Jean Mawhin (2006)
Journal of the European Mathematical Society
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We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation , when is arbitrary and or when . The proof uses upper and lower solutions and the Leray–Schauder degree.
Maciej Zakarczemny (2016)
Colloquium Mathematicae
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For every finite Abelian group Γ and for all , if there exists a solution of the equation in non-negative integers , where are positive integers, then the number of such solutions is estimated from below in the best possible way.
J. W. Heidel (1971)
Annales Polonici Mathematici
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J. W. Heidel (1973)
Annales Polonici Mathematici
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