A version of the law of large numbers
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.
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.
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...
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...
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].
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...
W. R. Utz (1971)
Annales Polonici Mathematici
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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.
David Grow (1987)
Colloquium Mathematicae
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Hasi Wulan, Kehe Zhu (2007)
Studia Mathematica
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Under mild conditions on the weight function K we characterize lacunary series in the so-called spaces.
Markus Passenbrunner (2011)
Studia Mathematica
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We identify the torus with the unit interval [0,1) and let n,ν ∈ ℕ with 0 ≤ ν ≤ n-1 and N:= n+ν. Then we define the (partially equally spaced) knots = ⎧ j/(2n) for j = 0,…,2ν, ⎨ ⎩ (j-ν)/n for for j = 2ν+1,…,N-1. Furthermore, given n,ν we let be the space of piecewise linear continuous functions on the torus with knots . Finally, let be the orthogonal projection operator from L²([0,1)) onto . The main result is . This shows in particular that the Lebesgue constant of the classical...
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...
Jaume Llibre, Víctor F. Sirvent (2016)
Mathematica Bohemica
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Let be a connected closed manifold and a self-map on . We say that is almost quasi-unipotent if every eigenvalue of the map (the induced map on the -th homology group of ) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of as eigenvalue of all the maps with odd is equal to the sum of the multiplicities of as eigenvalue of all the maps with even. We prove that if is having finitely many periodic points all of them...
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.
Ewa Strońska (2006)
Colloquium Mathematicae
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It is proved that the following conditions are equivalent: (a) f is an almost everywhere continuous function on ; (b) f = g + h, where g,h are strongly quasicontinuous on ; (c) f = c + gh, where c ∈ ℝ and g,h are strongly quasicontinuous on .
A. Szymański (1977)
Colloquium Mathematicae
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K. Orlov (1981)
Matematički Vesnik
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P. Srivastava, K. K. Azad (1981)
Matematički Vesnik
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Janusz Matkowski (1989)
Annales Polonici Mathematici
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Ralph McKenzie (1971)
Colloquium Mathematicae
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Stephan Baier (2004)
Acta Arithmetica
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А.М. Вершик (1972)
Zapiski naucnych seminarov Leningradskogo
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A. Pełczyński, H. Rosenthal (1975)
Studia Mathematica
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Chang-Shou Lin, Marcello Lucia (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider on a two-dimensional flat torus defined by a rectangular periodic cell the following equation It is well-known that the associated energy functional admits a minimizer for each . The present paper shows that these minimizers depend actually only on one variable. As a consequence, setting to be the first eigenvalue of the Laplacian on the torus, the minimizers are identically zero whenever . Our results hold more generally for solutions that...
A. Makowski (1964)
Matematički Vesnik
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