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Autor Muñoz-Fernández, Gustavo A. |
Documentos disponibles escritos por este autor (38)
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Muñoz-Fernández, Gustavo A. ; Sarantopoulos, Yannis ; Seoane-Sepúlveda, Juan B. | Heldermann Verlag | 2008Given a trinomial of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, we obtain, explicitly, the best possible constant M.,,(x) in the inequality vertical bar p'(x)vertical bar![]()
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Bernstein-markov type inequalities and other interesting estimates for polynomials on circle sectors
Jiménez Rodríguez, Pablo ; Muñoz-Fernández, Gustavo A. ; Pellegrine, D. ; Seoane-Sepúlveda, Juan B. | Board | 2017In this paper we study various polynomial inequalities for 2-homogeneous polynomials on the circular sector {rei: r ? [0,1]? [0, 2]}. In particular, we obtain sharp Bernstein and Markov inequalities for such polynomials, we calculate the polariz[...]![]()
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Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier Science | 2012-01In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question a[...]![]()
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Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Mathematical Assoc Amer | 2011-02It is well known that a function f : R -> R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2(c)-dimensional linear spaces of nowhere[...]![]()
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In this paper we find an alternative description of the Bochnak complexification of a real Hilbert space. This new interpretation of the Bochnak norm lets us give a characterization of a real inner product space.![]()
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In 1951 V. Jarnik constructed two continuous functions whose Volterra convolution is nowhere differentiable. We generalize Jarnik's results by proving that the set of such functions is maximal lineable. This would shed some light on a question p[...]![]()
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Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Elsevier | 2017In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy Littlewood constants for 2-homogeneous polynomials on l(p)(2) spaces, 2![]()
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Muñoz-Fernández, Gustavo A. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. | Taylor & Francis | 2012-05A classical inequality due to H. F. Bohnenblust and E. Hille states that for every positive integer n there is a constant C-n > 0 so that (Sigma(N)(i1,...,in=1) vertical bar U(e(i1), . . . , e(in))vertical bar(2n/n+1))(n+1/2n) C. The origina[...]![]()
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A mapping phi : [-1, 1] -> [0, infinity) is a curved majorant for a polynomial p in one real variable if vertical bar p(x)vertical bar![]()
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For each pair of numbers m, n epsilon N with m > n, we consider the norm on R-3 given by parallel to(a, b, c)parallel to m,n = sup{vertical bar ax(m) +bx(n) +C vertical bar: x epsilon [-1, 1]} for every (a, b, c) epsilon R-3. We investigate som[...]![]()
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Muñoz-Fernández, Gustavo A. ; Revesz, Szilard Gy. ; Seoane-Sepúlveda, Juan B. | Matematisk Inst | 2009If Delta stands for the region enclosed by the triangle in R(2) of vertices (0, 0), (0, 1) and (1, 0) (or simplex for short), we consider the space P((2)Delta) of the 2-homogeneous polynomials on R(2) endowed with the norm given by parallel to a[...]![]()
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Fenoy, Mar ; Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Sáez Maestro, Eva | De Gruyter Open Ltd | 2017This expository paper focuses on the study of extreme surjective functions in ??. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the[...]![]()
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Jiménez Rodríguez, P. ; Maghsoudi, S. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Belgian Mathematical Soc Triomphe | 2016It is known that there is not a two dimensional linear space in R-R every non-zero element of which is an injective function. Here, we generalize this result to arbitrarily large dimensions. We also study the convolution of non differentiable fu[...]![]()
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We give a condition for a family of functions to be lineable by means of its additivity. The novelty presented here is that we solve the lineability problem using a technique that is not constructive, as are most approaches to this problem. We r[...]![]()
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Araujo, G. ; Bernal-González, L. ; Muñoz-Fernández, Gustavo A. ; Prado-Bassas, J. A. ; Seoane-Sepúlveda, Juan B. | Polish Acad Sciencies Inst Mathematics | 2017We prove the existence of large algebraic structures - including large vector subspaces or infinitely generated free algebras - inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family o[...]![]()
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Muñoz-Fernández, Gustavo A. ; Palmberg, M. ; Puglisi, D. ; Seoane-Sepúlveda, Juan B. | Elsevier | 2008-06We show, among other results, that if lambda denotes the Lebesgue measure on the Borel sets in [0, 1] and X is an infinite dimensional Banach space, then the set of measures whose range is neither closed nor convex is lineable in ca(lambda, X). [...]![]()
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Lukes, J. ; Muñoz-Fernández, Gustavo A. ; Petracek, P. ; Seoane-Sepúlveda, Juan B. | Academic Press | 2016-11-15We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.![]()
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Lukes, J. ; Muñoz-Fernández, Gustavo A. ; Petracek, P. ; Seoane-Sepúlveda, Juan B. | Academic Press INC | 2016We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.![]()
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Diniz, D. ; Muñoz-Fernández, Gustavo A. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2014-02The Bohnenblust-Hille inequality was obtained in 1931 and ( in the case of real scalars) asserts that for every positive integer m there is a constant Cm so that ((N)Sigma(i1 , . . . , im=1)vertical bar T(e(i1) (,...,) e(im))vertical bar(2m/m+[...]![]()
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Bernal-González, L. ; Jimenez Rodriguez, G. A. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Springer | 2017It is proved the existence of large algebraic structures—including large vector subspaces or infinitely generated free algebras—inside the family of non-Lipschitz differentiable real functions with bounded gradient defined on special non-convex [...]![]()
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Jiménez Rodríguez, Pablo ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Elsevier | 2012-08-15Let E be a topological vector space and let us consider a property P. We say that the subset M of E formed by the vectors in E which satisfy P is ?-lineable (for certain cardinal ?, finite or infinite) if M ? {0} contains an infinite dimensional[...]![]()
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Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Núñez Alarcón, D. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. ; Serrano Rodríguez, D.M. | Springer | 2015-03We investigate the behavior of the constants of the polynomial Hardy-Littlewood inequality.![]()
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Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Nuñez-Alarcon, D. ; Pellagrino, D. ; Seoane-Sepúlveda, Juan B. ; Serrano-Rodriguez, D.M. | Birkhäuser Verlag | 2015We investigate the behavior of the constants of the polynomial Hardy-Littlewood inequality.![]()
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Campos, J.R. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. | Elsevier | 2015Abstract. It was recently proved by Bayart et al. that the complex polynomial Bohnenblust–Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if DR,m stands for the real Bohnenblu[...]![]()
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Jiménez Rodríguez, Pablo ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Belgian Mathematical Soc Triomphe | 2013-12Let E be a topological vector space and let us consider a property P. We say that the subset M of E formed by the vectors in E which satisfy 2 is mu-lineable (for certain cardinal mu, finite or infinite) if M U {0} contains an infinite dimensio[...]![]()
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Let parallel to . parallel to(infinity) denote the sup norm on [-1,1]. If x is an element of [-1,1] is fixed and M-m,M-n(x) is the best constant in vertical bar p'(x)vertical bar![]()
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Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. ; Weber, Andress | London Mathematical Society | 2012In this paper, we study the set of periods of (chaotic) strongly continuous semigroups. We prove a relationship between eigenvalues on the imaginary axis of the generator of a strongly continuous semigroup and the set of periods of the semigroup[...]![]()
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Araujo, G. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Heldermann Verlag | 2017A number of sharp inequalities are proved for the space P (2D (?/4)) of 2-homogeneous polynomials on ?2 endowed with the supremum norm on the sector D (?/4) := {ei? : ? ? [0, ?/4]}. Among the main results we can find sharp Bernstein and Markov i[...]![]()
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Azagra Rueda, Daniel ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. ; Sánchez de los Reyes, Víctor Manuel | Academic Press | 2009-06If f is continuous on the interval [a, b], g is Riemann integrable (resp. Lebesgue measurable) on the interval [alpha, beta] and g([alpha, beta]) subset of [a, b], then f o g is Riemann integrable (resp. measurable) on [alpha, beta]. A well-know[...]![]()
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Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Murillo Arcila, M. ; Seoane-Sepúlveda, Juan B. | Taylor & Francis | 2015In this paper we prove that the complex polynomial Bohnenblust-Hille constant for 2-homogeneous polynomials in C2 is exactly 4q 3 2 . We also give the exact value of the real polynomial Bohnenblust-Hille constant for 2-homogeneous polynomials in[...]![]()
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Gámez Merino, José Luis ; Muñoz-Fernández, Gustavo A. ; Sánchez, V.M. ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2010-11We find large algebraic structures inside the following sets of pathological functions: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) differentiable nowhere monoton[...]![]()
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Muñoz-Fernández, Gustavo A. ; Pellegrino, D. ; Seoane-Sepúlveda, Juan B. ; Weber, A. | Heldermann Verlag | 2014We consider the Banach space of two homogeneous polynomials endowed with the supremum norm parallel to . parallel to(D(beta)) over circle sectors D(beta) of angle beta for several values of beta is an element of [0, 2 pi]. We provide an explicit[...]![]()
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Diniz, D. ; Muñoz-Fernández, Gustavo A. ; Pellegrino, Daniel ; Seoane-Sepúlveda, Juan B. | Elsevier | 2012The search of sharp estimates for the constants in the Bohnenblust-Hille inequality, besides its challenging nature, has quite important applications in different fields of mathematics and physics. For homogeneous polynomials, it was recently sh[...]![]()
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Muñoz-Fernández, Gustavo A. ; Sarantopoulos, Y ; Seoane-Sepúlveda, Juan B. | American Mathematical Society | 2010K. Ball has proved the "complex plank problem": if (x(k))(k=1)(n) is a sequence of norm I vectors in a complex Hilbert space (H, (., .)), then there exists a unit vector x for which | | > = 1/root n, k = 1,...,n. In general, this resul[...]![]()
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This expository paper is devoted to the review of some very recent results concerning the set of periods of a chaotic operator T or a chaotic semigroup {T (t): t a parts per thousand yen 0} acting on a complex Banach space. We obtain information[...]![]()
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Let H be a two-dimensional complex Hilbert space and P(H-3) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, B-P(3H), from which we deduce that the unit sphere of P(H-3) is the disjo[...]![]()
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Grecu, B.C. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Academic Press- Elsevier Science | 2009-12If P is a polynomial on R of degree at most n, given by P(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar![]()
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Conejero, Jose A. ; Jiménez Rodríguez, P. ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. | Mathematical Association of America | 2014-01The Identity Theorem states that an analytic function (real or complex) on a connected domain is uniquely determined by its values on a sequence of distinct points that converge to a point of its domain. This result is not true in general in the[...]