Related papers: Wiener-Hopf factorizations and matrix-valued ortho…
We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial…
We construct Fourier transforms relating functions and distributions on finite height $p$-divisible rigid analytic groups and objects in a dual category of $\mathbb{Z}_p$-local systems with analyticity conditions. Our Fourier transforms are…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
Let $X$ denotes a discrete linearly ordered Abelian group, and let $X_+$ be the positive cone in $X$. In this note we compute the Fredholm index and study spectral properties of Wiener-Hopf operators $W_kg=1_{X_+}(k\ast g)$, $k\in l_2(X_+)$…
Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and…
We study analytically the coexistence of multiple periodic solutions and invariant tori in the general Van der Pol-Duffing oscillator equations. We use several results related to the averaging method in order to analytically obtain our…
Motivated by problems on the \'etale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the \'etale…
In this paper, by introducing new matrix operations and using a specific inverse relation, we establish the dual forms of the orthogonality relations for some well-known discrete and continuous $q$-orthogonal polynomials from the…
In this talk I discuss properties of the two Symanzik polynomials which characterise the integrand of an arbitrary multi-loop integral in its Feynman parametric form. Based on the construction from spanning forests and Laplacian matrices,…
We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based…
We discuss the recurrence coefficients of orthogonal polynomials with respect to a generalised sextic Freud weight \[\omega(x;t,\lambda)=|x|^{2\lambda+1}\exp\left(-x^6+tx^2\right),\qquad x\in\mathbb{R},\] with parameters $\lambda>-1$ and…
We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal…
We prove that for any compact toric symplectic manifold, if a Hamiltonian diffeomorphism admits more fixed points, counted homologically, than the total Betti number, then it has infinitely many simple periodic points. This provides a vast…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We…
In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight $w(x){\rm d}x = \log \frac{2k}{1-x}{\rm d}x$ on $(-1,1)$, $k > 1$, and verify a conjecture of…
Frank-Wolfe methods are popular for optimization over a polytope. One of the reasons is because they do not need projection onto the polytope but only linear optimization over it. To understand its complexity, Lacoste-Julien and Jaggi…
This article examines the asymptotic behavior of the Widom factors, denoted $\mathcal{W}_n$, for Chebyshev polynomials of finite unions of Jordan arcs. We prove that, in contrast to Widom's proposal, when dealing with a single smooth Jordan…
In 2017, Ono, Rolen, and Sprung [ORS17] answered problems of Manin [Man16] by defining zeta-polynomials $Z_f(s)$ for even weight newforms $f\in S_k(\Gamma_0(N)$; these polynomials can be defined by applying the "Rodriguez-Villegas…
H. Aoki showed that any symmetric formal Fourier-Jacobi series for the symplectic group Sp_2(Z) is the Fourier-Jacobi expansion of a holomorphic Siegel modular form. We prove an analogous result for vector valued symmetric formal…