Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of
J. Siciak (1969)
Annales Polonici Mathematici
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J. Siciak (1969)
Annales Polonici Mathematici
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Oleg Reinov, Qaisar Latif (2014)
Banach Center Publications
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Generalizing A. Grothendieck’s (1955) and V. B. Lidskiĭ’s (1959) trace formulas, we have shown in a recent paper that for p ∈ [1,∞] and s ∈ (0,1] with 1/s = 1 + |1/2-1/p| and for every s-nuclear operator T in every subspace of any -space the trace of T is well defined and equals the sum of all eigenvalues of T. Now, we obtain the analogous results for subspaces of quotients (equivalently: for quotients of subspaces) of -spaces.
M. K. Aouf (1989)
Matematički Vesnik
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A. Haldimann, H. Jarchow (2001)
Studia Mathematica
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The Nevanlinna algebras, , of this paper are the variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra of analytic functions f: → ℂ such that as |z| → 1 is the Fréchet envelope of . The corresponding algebra of analytic f: → ℂ such that is a complete metric space but fails to be a topological vector space....
Stefan Rolewicz (2009)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
Jean Schmets, Manuel Valdivia (2005)
Annales Polonici Mathematici
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We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ; (b) there is no continuous linear extension map from into ; (c) under some additional assumption on , there is an explicit extension map from into by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].
Luděk Zajíček (2023)
Commentationes Mathematicae Universitatis Carolinae
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Let be Banach spaces and a real function on . Let be the set of all points at which is partially Fréchet differentiable but is not Fréchet differentiable. Our results imply that if are Asplund spaces and is continuous (respectively Lipschitz) on , then is a first category set (respectively a -upper porous set). We also prove that if , are separable Banach spaces and is a Lipschitz mapping, then there exists a -upper porous set such that is Fréchet differentiable...
Jagannath Patel, Ashok Kumar Sahoo (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass of and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.
Edoardo Ballico (1981)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si dimostra che il complementare di un sottospazio analitico chiuso localmente intersezione completa di codimensione di una varietà di Stein è -completo.
Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv (2018)
Mathematica Bohemica
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We generalize some criteria of boundedness of -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).
Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let denote the class of analytic functions of the form in the open unit disc . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.
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.
Takashi Tsuboi (2009)
Annales scientifiques de l'École Normale Supérieure
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The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.
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...
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...
Wilhelmina Smajdor (1970)
Annales Polonici Mathematici
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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...
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;...
Elói Medina Galego, Christian Samuel (2013)
Studia Mathematica
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We completely determine the and C(K) spaces which are isomorphic to a subspace of , the projective tensor product of the classical space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...
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.