53 research outputs found
Products of polynomials in many variables
We study the product of two polynomials in many variables, in several norms, and show that under suitable assumptions this product can be bounded from below independently of the number of variables.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28840/1/0000675.pd
On the smoothness of L p of a positive vector measure
The final publication is available at Springer via http://dx.doi.org/10.1007/s00605-014-0666-7We investigate natural sufficient conditions for a space L p(m) of pintegrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a space, we prove that this is the case for instance if the Banach space where the vector measure takes its values is smooth. We give also some examples and show some applications of our results for determining norm attaining elements for operators between two spaces L p(m1) and Lq (m2) of positive vector measures m1 and m2.Professor Agud and professor Sanchez-Perez authors gratefully acknowledge the support of the Ministerio de Economia y Competitividad (Spain), under project #MTM2012-36740-c02-02. Professor Calabuig gratefully acknowledges the support of the Ministerio de Economia y Competitividad (Spain), under project #MTM2011-23164.Agud Albesa, L.; Calabuig Rodriguez, JM.; Sánchez PĂ©rez, EA. (2015). On the smoothness of L p of a positive vector measure. Monatshefte fĂĽr Mathematik. 178(3):329-343. https://doi.org/10.1007/s00605-014-0666-7S3293431783Beauzamy, B.: Introduction to Banach Spaces and Their Geometry. North-Holland, Amsterdam (1982)Diestel, J., Uhl, J.J.: Vector measures. In: Mathematical Surveys, vol. 15. AMS, Providence (1977)Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez-PĂ©rez, E.A.: Spaces of p-integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Ferrando, I., RodrĂguez, J.: The weak topology on L p of a vector measure. Topol. Appl. 155(13), 1439–1444 (2008)Godefroy, G.: Boundaries of a convex set and interpolation sets. Math. Ann. 277(2), 173–184 (1987)Howard, R., Schep, A.R.: Norms of positive operators on L p -spaces. Proc. Am. Math. Soc. 109(1), 135–146 (1990)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1977)Meyer-Nieberg, P.: Banach Latticces. Universitext, Springer-Verlag, Berlin (1991)Okada, S., Ricker, W.J., Sánchez-PĂ©rez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Advances and Applications, vol. 180. Birkhäuser Verlag, Basel (2008)Schep, A.: Products and factors of Banach function spaces. Positivity 14(2), 301–319 (2010
The Lee-Yang and P\'olya-Schur Programs. I. Linear Operators Preserving Stability
In 1952 Lee and Yang proposed the program of analyzing phase transitions in
terms of zeros of partition functions. Linear operators preserving
non-vanishing properties are essential in this program and various contexts in
complex analysis, probability theory, combinatorics, and matrix theory. We
characterize all linear operators on finite or infinite-dimensional spaces of
multivariate polynomials preserving the property of being non-vanishing
whenever the variables are in prescribed open circular domains. In particular,
this solves the higher dimensional counterpart of a long-standing
classification problem originating from classical works of Hermite, Laguerre,
Hurwitz and P\'olya-Schur on univariate polynomials with such properties.Comment: Final version, to appear in Inventiones Mathematicae; 27 pages, no
figures, LaTeX2
Bounded analytic functions in the Dirichlet space
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46275/1/209_2005_Article_BF01163287.pd
Strong convergence theorem for total quasi-Ď•-asymptotically nonexpansive mappings in a Banach space
Modified Proximal point algorithms for finding a zero point of maximal monotone operators, generalized mixed equilibrium problems and variational inequalities
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