2009
http://publications.mfo.de/handle/mfo/1341
Wed, 06 Nov 2024 08:45:35 GMT2024-11-06T08:45:35ZAlternative iterative methods for nonexpansive mappings, rates of convergence and applications
http://publications.mfo.de/handle/mfo/1227
Alternative iterative methods for nonexpansive mappings, rates of convergence and applications
Colao, Vittorio; Leuştean, Laurenţiu; López, Genaro; Martín Márquez, Victoria
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.
OWLF 2008
Thu, 01 Jan 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12272009-01-01T00:00:00ZColao, VittorioLeuştean, LaurenţiuLópez, GenaroMartín Márquez, VictoriaAlternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.Proof mining in metric fixed point theory and ergodic theory
http://publications.mfo.de/handle/mfo/1226
Proof mining in metric fixed point theory and ergodic theory
Leuştean, Laurenţiu
In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach spaces.
OWLF 2009
Thu, 01 Jan 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12262009-01-01T00:00:00ZLeuştean, LaurenţiuIn this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach spaces.Minimal Riesz energy on the sphere for axis-supported external fields
http://publications.mfo.de/handle/mfo/1225
Minimal Riesz energy on the sphere for axis-supported external fields
Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B.
Abstract. We investigate the minimal Riesz $s$-energy problem for positive
measures on the d-dimensional unit sphere $\mathbb{S}^d$
in the presence of an external
field induced by a point charge, and more generally by a line charge. The model
interaction is that of Riesz potentials $|x−y|^{−s}$ with $d−2 ≤ s < d$. For a given
axis-supported external field, the support and the density of the corresponding
extremal measure on $\mathbb{S}^d$
is determined. The special case $s = d − 2$ yields
interesting phenomena, which we investigate in detail. A weak$^∗$ asymptotic
analysis is provided as $s → (d − 2)^+$.
OWLF 2008
Thu, 01 Jan 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12252009-01-01T00:00:00ZBrauchart, Johann S.Dragnev, Peter D.Saff, Edward B.Abstract. We investigate the minimal Riesz $s$-energy problem for positive
measures on the d-dimensional unit sphere $\mathbb{S}^d$
in the presence of an external
field induced by a point charge, and more generally by a line charge. The model
interaction is that of Riesz potentials $|x−y|^{−s}$ with $d−2 ≤ s < d$. For a given
axis-supported external field, the support and the density of the corresponding
extremal measure on $\mathbb{S}^d$
is determined. The special case $s = d − 2$ yields
interesting phenomena, which we investigate in detail. A weak$^∗$ asymptotic
analysis is provided as $s → (d − 2)^+$.Heisenberg-Weyl algebra revisited: combinatorics of words and paths
http://publications.mfo.de/handle/mfo/1224
Heisenberg-Weyl algebra revisited: combinatorics of words and paths
Blasiak, Pawel; Duchamp, Gérard H. E.; Horzela, Andrzej; Penson, Karol A.; Solomon, Allan I.
The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From this starting point we explore a combinatorial underpinning of the Heisenberg–Weyl algebra, which offers novel perspectives, methods and applications.
OWLF 2008
Thu, 01 Jan 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12242009-01-01T00:00:00ZBlasiak, PawelDuchamp, Gérard H. E.Horzela, AndrzejPenson, Karol A.Solomon, Allan I.The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From this starting point we explore a combinatorial underpinning of the Heisenberg–Weyl algebra, which offers novel perspectives, methods and applications.Geometric quantization of integrable systems with hyperbolic singularities
http://publications.mfo.de/handle/mfo/1223
Geometric quantization of integrable systems with hyperbolic singularities
Hamilton, Mark D.; Miranda, Eva
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.
OWLF 2008
Thu, 01 Jan 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12232009-01-01T00:00:00ZHamilton, Mark D.Miranda, EvaWe construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.Optimal bounds for the colored Tverberg Problem
http://publications.mfo.de/handle/mfo/1161
Optimal bounds for the colored Tverberg Problem
Blagojevic, Pavle V. M.; Matschke, Benjamin; Ziegler, Günter M.
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory
Research in Pairs 2009
Fri, 20 Mar 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/11612009-03-20T00:00:00ZBlagojevic, Pavle V. M.Matschke, BenjaminZiegler, Günter M.We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theoryWeighted Fourier inequalities for radial functions
http://publications.mfo.de/handle/mfo/1160
Weighted Fourier inequalities for radial functions
Gorbachev, D.; Liflyand, E.; Tichonovič, S. V.
Weighted $L^p(\mathbb{R}^n) \to L^q(\mathbb{R}^n)$ Fourier inequalities are studied. We prove Pitt-Boas type results on integrability with power weights of the Fourier transform of a radial function.
Research in Pairs 2009
Thu, 19 Mar 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/11602009-03-19T00:00:00ZGorbachev, D.Liflyand, E.Tichonovič, S. V.Weighted $L^p(\mathbb{R}^n) \to L^q(\mathbb{R}^n)$ Fourier inequalities are studied. We prove Pitt-Boas type results on integrability with power weights of the Fourier transform of a radial function.A new counting function for the zeros of holomorphic curves
http://publications.mfo.de/handle/mfo/1159
A new counting function for the zeros of holomorphic curves
Anderson, J. M.; Hinkkanen, Aimo
Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the zero of a linear combination of the functions $f_1,..., f_p$ at any point where such a linear combination vanishes, and, if all the $f_1,..., f_p$ are polynomials, also at infinity. This enables us to formulate an inequality, which sometimes holds as an identity, that sharpens the classical results of Cartan and others.
Research in Pairs 2009
Wed, 18 Mar 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/11592009-03-18T00:00:00ZAnderson, J. M.Hinkkanen, AimoLet $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the zero of a linear combination of the functions $f_1,..., f_p$ at any point where such a linear combination vanishes, and, if all the $f_1,..., f_p$ are polynomials, also at infinity. This enables us to formulate an inequality, which sometimes holds as an identity, that sharpens the classical results of Cartan and others.Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich
http://publications.mfo.de/handle/mfo/1158
Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich
Di Francesco, Philippe; Kedem, Rinat
We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for non-commutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials in the initial cluster variables. We prove this by use of a non-commutative version of the path models which we used for the commutative case.
Research in Pairs 2009
Tue, 17 Mar 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/11582009-03-17T00:00:00ZDi Francesco, PhilippeKedem, RinatWe prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for non-commutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials in the initial cluster variables. We prove this by use of a non-commutative version of the path models which we used for the commutative case.On Siegel modular forms of level p and their properties mod p
http://publications.mfo.de/handle/mfo/1157
On Siegel modular forms of level p and their properties mod p
Böcherer, Siegfried; Nagaoka, Shoyu
Using theta series we construct Siegel modular forms of level p which behave well modulo $p$ in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 are congruent mod $p$ to level one modular forms of weight $p+1$; in particular, this is true for Yoshidal lifts of level $p$.
Research in Pairs 2008
Mon, 16 Mar 2009 00:00:00 GMThttp://publications.mfo.de/handle/mfo/11572009-03-16T00:00:00ZBöcherer, SiegfriedNagaoka, ShoyuUsing theta series we construct Siegel modular forms of level p which behave well modulo $p$ in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 are congruent mod $p$ to level one modular forms of weight $p+1$; in particular, this is true for Yoshidal lifts of level $p$.