相关论文: On multi-symmetric functions and transportation po…
It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and…
Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric kind is a common generalization of Schur functions, Macdonald spherical functions, and Jack polynomials. We use the…
A theoretical investigation of quantum-transport phenomena in mesoscopic systems is presented. In particular, a generalization to ``open systems'' of the well-known semiconductor Bloch equations is proposed. The presence of spatial boundary…
In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable…
This paper presents an algebraic construction of Euler-Maclaurin formulas for polytopes. The formulas obtained generalize and unite the previous lattice point formulas of Morelli and Pommersheim-Thomas, and the Euler-Maclaurin formulas of…
We discuss a space of Young measures in connection with some variational problems. We use it to present a proof of the Theorem of Tonelli on the existence of minimizing curves. We generalize a recent result of Ambrosio, Gigli and Savar\'e…
In a recent paper with Sahi and Stokman, we introduced quasi-polynomial generalizations of Macdonald polynomials for arbitrary root systems via a new class of representations of the double affine Hecke algebra. These objects depend on a…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the…
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew…
We study square integrable functions on the metaplectic group and functions on the space of unitary symmetric matrices. We relate them using the oscillator representations.
An expository hitchhikers guide to some theorems in mathematics.
In [arXiv 0811.3913] the authors introduced the notion of quasi-polynomial function as being a mapping f: X^n -> X defined and valued on a bounded chain X and which can be factorized as f(x_1,...,x_n)=p(phi(x_1),...,phi(x_n)), where p is a…
The regularity theory of the Campanato space $\mathcal{L}^{(q,\lambda)}_k(\Omega)$ has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from…
Some classical mass transportation problems are investigated in a finitely additive setting. Let $\Omega=\prod_{i=1}^n\Omega_i$ and $\mathcal{A}=\otimes_{i=1}^n\mathcal{A}_i$, where $(\Omega_i,\mathcal{A}_i,\mu_i)$ is a ($\sigma$-additive)…
We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These…
We analyze the effect of symmetrization in the theory of multiple orthogonal polynomials. For a symmetric sequence of type II multiple orthogonal polynomials satisfying a high-term recurrence relation, we fully characterize the Weyl…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
We systematically study wreath product Schur functions and give a combinatorial construction using colored partitions and tableaux. The Pieri rule and the Littlewood-Richardson rule are studied. We also discuss the connection with…
We present a friendly introduction to the very detailed results in [9,10,11] and as an illustration we discuss here the issue of {\em linearization of products}. We find some interesting new phenomena.