Related papers: Fatou's interpolation theorem implies the Rudin-Ca…

In this paper we prove the WALA conjecture.

We prove an inequality for the f-vectors of anti-self-polar polytopes conjectured by Katz in 1989. The proof uses Kalai's combinatorial inequality based on a result of Whiteley. The inequality can also be obtained from the results of…

In this article we give a survey of the various forms of Berthelot's conjecture and some of the implications between them. By proving some comparison results between pushforwards of overconvergent isocrystals and those of arithmetic…

In this work, we show that the complex interpolation space is the same by the two methods.

The purpose of this expository paper is to explain how the Fargues-Fontaine curve and its decomposition into a punctured curve and the formal neighborhood of the puncture naturally arise from various forms of topological cyclic homology and…

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of…

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…

We prove a finiteness principle for interpolation of data by nonnegative Cm functions. Our result raises the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function F is required to…

This dissertation entitled "Fatou's No Wandering Domain Conjecture : Sullivan's Proof" contains a comprehensive study of the Dynamical Partition of the Riemann Sphere and a complementary analysis of the work done by Dennis Sullivan.

The Fluctuation Theorem (FT) gives an analytic expression for the probability, in a nonequilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the Second…

The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We prove a version of the Fatou theorem for bounded functions with bounded d_J-bar diferential on wedge-type domains in an almost complex manifold.

We treat interpolation for various logics.

We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.

We extend the interpolation property of the Lubin-Tate regulator map from [SV24] to Artin characters and show a reciprocity law in the sense of Cherbonnier-Colmez. This allows us to provide a new proof of Kato's explicit reciprocity law for…

The aim of the paper is to establish a certain logic corresponding to lattice effect algebras. First, we answer a natural question whether a lattice effect algebra can be represented by means of a groupoid-like structure. We establish a…

Around 2001 we classified the Leonard systems up to isomorphism. The proof was lengthy and involved considerable computation. In this paper we give a proof that is shorter and involves minimal computation. We also give a comprehensive…

The Butterfly lemma we present can be considered a reiteration theorem for differentials generated from a complex interpolation process for families of K\"othe spaces. The lemma will be used to clarify the effect of different configurations…