The Gibbs phenomenon and Lebesgue constants for regular means
V. Swaminathan (1977)
Matematički Vesnik
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V. Swaminathan (1977)
Matematički Vesnik
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Dušan Pokorný, Marc Rauch (2022)
Commentationes Mathematicae Universitatis Carolinae
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We deal with the so-called Ahlfors regular sets (also known as -regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit exist, where is an -regular set and is for instance the -packing number of ?
John Krueger (2008)
Fundamenta Mathematicae
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We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of , where κ ⊆ X. Suppose μ < κ, , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in which are internally club but not internally approachable.
Yoshishige Haraoka (2012)
Banach Center Publications
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For a Fuchsian system , (F) being distinct points in ℂ and , the number α of accessory parameters is determined by the spectral types , where . We call the set of α parameters a regular coordinate if all entries of the are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues...
Tadeusz Maćkowiak
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CONTENTSIntroduction.......................................................................................................51. Preliminaries.................................................................................................6 A. Mappings....................................................................................................6 B. Arc-like continua.........................................................................................8 C. Pseudosuspensions...................................................................................8 D....
R. Frankiewicz (1978)
Colloquium Mathematicae
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Alejandro Illanes (2016)
Commentationes Mathematicae Universitatis Carolinae
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A metric continuum is said to be continuously homogeneous provided that for every two points there exists a continuous surjective function such that . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum such that the hyperspace of subcontinua of , , is not continuously homogeneous.
Tomasz Słonka (2012)
Colloquium Mathematicae
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We show that if n is a positive integer and , then for every positive integer m and for every real constant c > 0 there are functions such that and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that for .
Ivan Lončar (2017)
Archivum Mathematicum
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For metrizable continua, there exists the well-known notion of a Whitney map. If is a nonempty, compact, and metric space, then any Whitney map for any closed subset of can be extended to a Whitney map for [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.
V. Farmaki, V. Nestoridis (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence of scalars, there exists a subsequence such that either every subsequence of defines a universal series, or no subsequence of defines a universal series. In particular examples we decide which of the two cases holds.
Michael G. Charalambous, Jerzy Krzempek (2010)
Fundamenta Mathematicae
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For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum such that (a) ; (b) ; (c) ; (d) if β < ω(⁺), then is separable and first countable; (e) if n = 1, then can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then can be made chainable and hereditarily indecomposable. In...
William Fleissner, Lynne Yengulalp (2013)
Fundamenta Mathematicae
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Let M be a metrizable group. Let G be a dense subgroup of . We prove that if G is domain representable, then . The following corollaries answer open questions. If X is completely regular and is domain representable, then X is discrete. If X is zero-dimensional, T₂, and is subcompact, then X is discrete.
N. Kalamidas, Th. Zachariades (1989)
Colloquium Mathematicae
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M. Cristina Ronconi (2009)
Bollettino dell'Unione Matematica Italiana
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The range of the bigenus is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with : The examples in the literature have . In the present paper we present a non-singular threefold with ; ; the bicanonical map is stably birational.
Takashi Noiri (1981)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Se ed sono spazi topologici, una funzione è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di in un insieme chiuso di . Si dimostra che una funzione regolarmente chiusa risulta chiusa se è normale.
Tien-Cuong Dinh, Nessim Sibony (2008)
Annales scientifiques de l'École Normale Supérieure
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Let be a non-invertible holomorphic endomorphism of a projective space and its iterate of order . We prove that the pull-back by of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to when tends to infinity. We also give an analogous result for the pull-back of positive closed -currents and a similar result for regular polynomial automorphisms of .
S. Moll (2008)
Banach Center Publications
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Let X be a completely regular Hausdorff topological space and the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of .
Graziano Gentili, Simon Salamon, Caterina Stoppato (2014)
Journal of the European Mathematical Society
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The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains of . When is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space .
Silvano Delladio (2008)
Bollettino dell'Unione Matematica Italiana
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We prove a result about the rectifiability of class of the set of regular values (in the sense of Clarke) of a Lipschitz map with
Olivier Debarre (2006)
Bulletin de la Société Mathématique de France
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To any finite covering of degree between smooth complex projective manifolds, one associates a vector bundle of rank on whose total space contains . It is known that is ample when is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when is a simple abelian variety and does not factor through any nontrivial isogeny . This result is obtained by showing that is -regular...
Mohammed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou, Filomena Pacella (2005)
Journal of the European Mathematical Society
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We consider the Yamabe type family of problems , in , on , where is an annulus-shaped domain of , , which becomes thinner as . We show that for every solution , the energy as well as the Morse index tend to infinity as . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on , a half-space or an infinite strip. Our argument also involves a Liouville...
Jiří M. Tomáš (2017)
Czechoslovak Mathematical Journal
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Let be an -dimensional manifold and a Weil algebra of height . We prove that any -covelocity , is determined by its values over arbitrary regular and under the first jet projection linearly independent elements of . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result without coordinate computations, which improves and generalizes the partial...
Victor Galaktionov (2004)
Journal of the European Mathematical Society
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We consider th-order semilinear parabolic equations in , with Dirac’s mass as the initial function. We show that for , the Cauchy problem admits a solution which is bounded and smooth for small , while for such a local in time solution does not exist. This leads to a boundary layer phenomenon in constructing a proper solution via regular approximations.
Klaus Denecke, Prakit Jampachon (2006)
Discussiones Mathematicae - General Algebra and Applications
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Defining an (n+1)-ary superposition operation on the set of all n-ary terms of type τ, one obtains an algebra of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation there are different possibilities to define binary associative operations on the set and on the cartesian power . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative...
Christina Brech, Piotr Koszmider (2014)
Fundamenta Mathematicae
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This paper is concerned with the isomorphic structure of the Banach space and how it depends on combinatorial tools whose existence is consistent with but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that does not have an orthogonal -decomposition, that is, it is not of the form for any Banach space X. The main local result is that it is consistent that does not embed isomorphically into , where is the cardinality of the continuum,...