A generalized radial integration by parts formula and its applications to Caffarelli-Kohn-Nirenberg inequalities [0.03%]
广义径向积分分部公式及其在Caffarelli-Kohn-Nirenberg不等式中的应用
Giovanni Di Fratta,Alberto Fiorenza
Giovanni Di Fratta
This paper builds upon the Caffarelli-Kohn-Nirenberg (CKN) weighted interpolation inequalities, which are fundamental tools in partial differential equations and geometric analysis for establishing relationships between functions and their ...
Eduardo S Zeron,Paul M Gauthier
Eduardo S Zeron
We show that the analytic content λ ( · ) is neither subadditive nor semiadditive. To be precise, for compact sets K in the complex plane, λ ( K ) is the K-uniform distance from the complex conjugation to the algebra of all...
Javad Mashreghi,Marek Ptak,William T Ross
Javad Mashreghi
If U is a unitary operator on a separable complex Hilbert space H, an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive, isometry on H) for which CUC=U∗. In this paper, we fix a unitary ...
Javad Mashreghi,Marek Ptak,William T Ross
Javad Mashreghi
For a unitary operator U on a separable complex Hilbert space H, we describe the set Cc(U) of all conjugations C (antilinear, isometric, and involutive maps) on H for which CUC=U. As this set might be empty, we also show that Cc(U)≠&#...
A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation [0.03%]
环面上的标量Riemann-Hilbert问题及其在KdV方程中的应用
Mateusz Piorkowski,Gerald Teschl
Mateusz Piorkowski
We take a closer look at the Riemann-Hilbert problem associated to one-gap solutions of the Korteweg-de Vries equation. To gain more insight, we reformulate it as a scalar Riemann-Hilbert problem on the torus. This enables us to derive dedu...
Modulus of continuity of controlled Loewner-Kufarev equations and random matrices [0.03%]
受控Loewner-Kufarev方程和随机矩阵的模连续性
Takafumi Amaba,Roland Friedrich
Takafumi Amaba
First we introduce the two tau-functions which appeared either as the τ -function of the integrable hierarchy governing the Riemann mapping of Jordan curves or in conformal field theory and the universal Grassmannian. Then we discuss v...
Jonathan Andersson,Samia Ghersheen,Vladimir Kozlov et al.
Jonathan Andersson et al.
In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the under...
Diagonalization of the finite Hilbert transform on two adjacent intervals: the Riemann-Hilbert approach [0.03%]
有限希尔伯特变换的对角化：里曼-希尔伯特方法
Marco Bertola,Elliot Blackstone,Alexander Katsevich et al.
Marco Bertola et al.
In this paper we study the spectra of bounded self-adjoint linear operators that are related to finite Hilbert transforms H L : L 2 ( [ b L , 0 ] ) → L 2 ( [ 0 , b R ] ) and H R : L 2 ( [ 0 , b R ] ) → L 2 ( [ b L , 0 ] ) ...