On the classification of real mono-germs of corank one and codimension one
Kevin Houston (2004)
Banach Center Publications
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Corank one mono-germs , n < p, of -codimension one are classified by giving an explicit normal form.
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Kevin Houston (2004)
Banach Center Publications
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Corank one mono-germs , n < p, of -codimension one are classified by giving an explicit normal form.
Roberto Luiz Soraggi (1981)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Sia uno spazio riflessivo e sia un compatto di . Si dimostra che lo spazio dei germi olomorfi su , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.
J. H. Rieger, M. A. S. Ruas, R. Wik Atique (2008)
Banach Center Publications
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A stable deformation of a real map-germ is said to be an M-deformation if all isolated stable (local and multi-local) singularities of its complexification are real. A related notion is that of a good real perturbation of f (studied e.g. by Mond and his coworkers) for which the homology of the image (for n < p) or discriminant (for n ≥ p) of coincides with that of . The class of map germs having an M-deformation is, in some sense, much larger than the one having a good...
Roberto Luiz Soraggi (1981)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Sia uno spazio riflessivo e sia un compatto di . Si dimostra che lo spazio dei germi olomorfi su , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.
Liguang Liu, Dachun Yang (2009)
Studia Mathematica
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Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space to a quasi-Banach space ℬ if and only if sup: a is an infinitely differentiable (p,q,s)-atom of < ∞, where the (p,q,s)-atom of is as defined by Han, Paluszyński and Weiss.
N. Honda, G. Morando (2011)
Bulletin de la Société Mathématique de France
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In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold . Then, we define stratified ultradistributions of Beurling and Roumieu type on . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to . Second,...
William Alexandre, Emmanuel Mazzilli (2014)
Annales de l’institut Fourier
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We give in a real analytic almost complex structure , a real analytic hypersurface and a vector in the Levi null set at of , such that there is no germ of -holomorphic disc included in with and , although the Levi form of has constant rank. Then for any hypersurface and any complex structure , we give sufficient conditions under which there exists such a germ of disc.
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...
Hassan Sfouli (2014)
Annales Polonici Mathematici
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Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let and f̂ be its Taylor series at . Split the set of exponents into two disjoint subsets A and B, , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some...
Zbigniew Lipecki (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We give some criteria for order boundedness of in , in the general case as well as for atomic . Order boundedness implies weak compactness of . We show that the converse implication holds under some assumptions on , and or alone, but not in general.
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 .
Laurent Meersseman (2011)
Annales scientifiques de l'École Normale Supérieure
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Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of in , for some ) or differentiable (parametrized by an open neighborhood of in , for some ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point of the parameter space, the fiber over of the first family is biholomorphic to the fiber over of the second family. Then, under which conditions...
A. Bouziad, E. Sukhacheva (2017)
Commentationes Mathematicae Universitatis Carolinae
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For a subset of the real line , Hattori space is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on which are sufficient and necessary for to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...
Anna Kamińska, Lech Maligranda (2004)
Studia Mathematica
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We study order convexity and concavity of quasi-Banach Lorentz spaces , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that contains an order isomorphic copy of . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for . We conclude with a characterization of the type and cotype of in the case when is a normable space.
J. Siciak (1969)
Annales Polonici Mathematici
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M. K. Aouf (1989)
Matematički Vesnik
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Teresa Monteiro Fernandes, Luca Prelli (2014)
Fundamenta Mathematicae
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Given a real analytic manifold Y, denote by the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor on the category of sheaves on and study its properties. Roughly speaking, is a sheaf on . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.
Zbigniew Lipecki (2017)
Commentationes Mathematicae Universitatis Carolinae
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Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We show that is order bounded if and only if it is contained in a principal ideal in if and only if it is weakly compact and is contained in a principal ideal in . We also establish some criteria for the coincidence of the ideals, in , generated by and .
Shih-Hung Chang (1976)
Annales Polonici Mathematici
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Joseph Cima, Raymond Mortini (1995)
Studia Mathematica
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It is shown that the Bourgain algebra of the disk algebra A() with respect to is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is .
Abdelhafed Elkhadiri (2011)
Annales Polonici Mathematici
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Let R be a real closed field, and denote by the ring of germs, at the origin of Rⁿ, of functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring with some natural properties. We prove that, for each n ∈ ℕ, is a noetherian ring and if R = ℝ (the field of real numbers), then , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring . ...
Michel Belliart (2007)
Bulletin de la Société Mathématique de France
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Plane -webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two -webs, are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable -webs, however, there always exists a nonmeasurable conjugacy;...
Francesca Acquistapace, A. Díaz-Cano (2011)
Journal of the European Mathematical Society
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We prove that any divisor of a global analytic set has a generic equation, that is, there is an analytic function vanishing on with multiplicity one along each irreducible component of . We also prove that there are functions with arbitrary multiplicities along . The main result states that if is pure dimensional, is locally principal, is not connected and represents the zero class in then the divisor is globally principal.
Abtin Daghighi, Frank Wikström (2016)
Czechoslovak Mathematical Journal
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Let be a bounded, simply connected -convex domain. Let and let be a function on which is separately -smooth with respect to (by which we mean jointly -smooth with respect to , ). If is -analytic on , then is -analytic on . The result is well-known for the case , , even when a priori is only known to be continuous.