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Some completely monotonic functions involving the $q$-gamma function
monotonic functions the $q$-gamma function
2010/11/19
We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.
Maximal theorems and square functions for analytic operators on Lp-spaces
Maximal theorems square functions analytic operators on Lp-spaces
2010/11/11
Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive intege...
$\ell^2$-Linear Independence for the System of Integer Translates of a Square Integrable Function
Linear Independence Square Integrable Function
2010/11/15
We prove that if the system of integer translates of a square integrable function is $\ell^2$-linear independent then its periodization function is strictly positive almost everywhere. Indeed we show...
Eigenvalues and eigenfunctions of the Laplacian via inverse iteration with shift
Eigenvalues and eigenfunctions the Laplacian
2010/11/19
In this paper we present an iterative method inspired by the inverse iteration with shift technique of finite linear algebra designed to find the eigenvalues and eigenfunctions of the Laplacian with h...
Concave Majorants of Random Walks and Related Poisson Processes
Concave Majorants Related Poisson Processes
2010/11/19
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providin...
Hilbert series of PI relatively free G-graded algebras are rational functions
free G-graded algebras rational functions
2010/11/19
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F be the corresponding free...
Construction of homogeneous Lagrangian submanifolds in $\CP^n$ and Hamiltonian stability
Lagrangian submanifolds Hamiltonian stability
2010/11/19
We apply the concept of castling transform of prehomogeneous vector spaces to produce new examples of minimal homogeneous Lagrangian submanifolds in the complex projective space. Furthermore we verify...
Testing the functional equations of a high-degree Euler product
the functional equations a high-degree Euler product
2010/11/11
We study the L-functions associated to Siegel modular forms (equivalently, automorphic representations of ${\rm GSp}(4,\mathbb{A}_{\mathbb{Q}})$) both theoretically and numerically. For the L-functio...
Zeros of nonpositive type of generalized Nevanlinna functions with one negative square
Nevanlinna functions negative square
2010/11/15
A generalized Nevanlinna function $Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation d...
Level Sets of the Takagi Function: Generic Level Sets
the Takagi Function Generic Level Sets
2010/11/19
The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. This paper studies the level sets L(y) = {x : \tau (x) = y} of the Takagi funct...
Optimising a nonlinear utility function in multi-objective integer programming
nonlinear utility function multi-objective integer programming
2010/11/15
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer nondominated set. Our approach is based on identifying and updating bounds on th...
In this paper we study linear correlations of the divisor function tau(n) = sum_{d|n} 1 using methods developed by Green and Tao. For example, we obtain an asymptotic for sum_{n,d} tau(n) tau(n+d) ......
Toric plurisubharmonic functions and analytic adjoint ideal sheaves
Toric plurisubharmonic functions analytic adjoint ideal sheaves
2010/11/19
In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier...
Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
correlation functions the one-dimensional Bose gas
2010/11/19
We describe a Bethe ansatz based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density-density correlation fun...
On the power of function values for the approximation problem in various settings
function values the approximation problem various settings
2010/11/22
This is an expository paper on approximating functions from general Hilbert or Banach spaces in the worst case, average case and randomized settings with error measured in the $L_p$ sense. We define ...