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Extensions of homogeneous polynomials ON c(0)(l(2)(i))
(VERSITA, 2008)
We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a ...
Hypercyclic homogeneous polynomials on H(C)
(Academic Press Inc Elsevier Science, 2018-02)
It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic ...
Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2
(2016-02-01)
We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class ...
M-structures in vector-valued polynomial spaces
(Heldermann Verlag, 2012-12)
This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; ...
Where do Homogeneous Polynomials Attain their Norm?
(Universidad de San Andrés. Departamento de Matemáticas y Ciencias, 2000-03)
Ideal structures in vector-valued polynomial spaces
(Banach Mathematical Research Group, 2016-10)
This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of n-homogeneous polynomials, Pw(nE,F), which are weakly ...
O adjunto de um polinômio homogêneo contínuo entre espaços de BanachThe adjoint of a continuous homogeneous polynomial on Banach spaces
(Universidade Federal de UberlândiaBRPrograma de Pós-graduação em MatemáticaCiências Exatas e da TerraUFU, 2016)
Lower bounds for norms of products of polynomials on Lp spaces
(Polish Acad Sciences Inst Mathematics, 2013-01)
For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on Lp(µ), whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily ...
On the measure of polynomials attaining maxima on a vertex
(Element, 2019-03)
We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of ...
On the convergence of random polynomials and multilinear forms
(Academic Press Inc Elsevier Science, 2011-10)
We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is ...