Related papers: Interpolation, box splines, and lattice points in …
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
Following Aguil\'{o}-Su\~{n}er-Torrens (2008), Koles\'{a}rov\'{a}-Mesiar-Mordelov\'{a}-Sempi (2006) and Mayor-Su\~{n}er-Torrens (2005), we continue to develop a theory of matrix representation for discrete copulas. To be more precise, we…
This is a study of inner-outer factorization for analytic matrix-valued functions focusing on representations of the factors in terms of multiplicative integrals. Included is a brief introduction to the theory of multiplicative integrals…
Given an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\bar z\bar{H^p}$ be the associated star-invariant subspace of the Hardy space $H^p$. Also, we put $K_{*\theta}:=K^2_\theta\cap{\rm BMO}$. Assuming that…
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…
We consider entire matrix functions $A(z)$ taking values in $\operatorname{SL}(2,\mathbb C)$. These map pairs of Herglotz functions by acting pointwise as linear fractional transformations. The main examples of such Toda maps are provided…
Let $S$ be a non-empty, closed subspace of a locally compact group $G$ that is a subsemigroup of $G$. Suppose that $X, Y$, and $Z$ are Banach lattices that are vector sublattices of the order dual $\mathrm{C}_{\mathrm{c}}(S,\mathbb R)^\sim$…
We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced…
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We give a representation--theoretic interpretation of recent discovered coupled soliton equations using vertex operators construction of affinization of not simple but quadratic Lie algebras. In this setup we are able to obtain new…
We extend to a situation involving matrix valued orthogonal polynomials a scalar result that originates in work of Claude Shannon and a ground-breaking series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's.…
Let $\mathcal{O}(U)$ denote the algebra of holomorphic functions on an open subset $U\subset\mathbb{C}^n$ and $Z\subset\mathcal{O}(U)$ its finite-dimensional vector subspace. By the theory of least space of de Boor and Ron, there exists a…
This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.
In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric $3$-dimensional polytopes, by showing they are covered by lattice parallelepipeds and…
We extract an exact formula relating the number of lattice points in an expanding region of a complex semi-simple symmetric space and the automorphic spectrum from a spectral identity, which is obtained by producing two expressions for the…
We continue the algebraic investigation of PBZ*-lattices, a notion introduced in [12] in order to obtain insights into the structure of certain algebras of effects of a Hilbert space, lattice-ordered under the spectral ordering.
In this paper we propose a unified approach, based on limiting interpolation, to investigate the embeddings for the Sobolev space $(\dot{W}^k_p(\mathcal{X}))_0, \, \mathcal{X} \in \{\mathbb{R}^d, \mathbb{T}^d, \Omega\}$, in the subcritical…
We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be…
Lattice calculations of matrix elements involving heavy-light quark bilinears are of interest in calculating a variety of properties of B and D mesons, including decay constants and mixing parameters. A large source of uncertainty in the…