相关论文: A multidimensional version of Levin's Secular Cons…
Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…
We study the Eisenstein series and constant term functors in the framework of geometric theory of automorphic functions. Our main result says that for a parabolic P in G with Levi quotient M, the !-constant term functor CT_!:D-mod(Bun_G)->…
Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…
The Rankin-Selberg method for studying Langlands' automorphic $L$-functions is to find integral representations, involving certain Fourier coefficients of cusp forms and Eisenstein series, for these functions. In this thesis we develop the…
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
In this paper we study in details the properties of the duality product of multivectors and multiforms (used in the definition of the hyperbolic Clifford algebra of multivefors) and introduce the theory of the k multivector and l multiform…
The Poincar\'e-Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of $C^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly…
We prove a subconvexity bound in the conductor aspect for $L(s,f,\chi)$ where $f$ is a half integer weight modular form. This $L$-function has analytic continuation and functional equation, but no Euler product. Due to the lack of an Euler…
We study Ptolemy constant and uniformity constant in various plane domains including triangles, quadrilaterals and ellipses.
We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these…
The Euler-Kronecker constants related to congruences of Fourier coefficients of modular forms that have been computed so far, involve logarithmic derivatives of Dirichlet $L$-series as most complicated functions (to the best of our…
Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of…
We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof of Cardy's formula, in order to determine…
We work in a discrete model of the nonlinear Fourier transform (following the terminology of Tao and Thiele), which appears in the study of orthogonal polynomials on the unit circle. The corresponding nonlinear variant of the…
We pose a normal form of transition functions along some Levi-flat hypersurfaces obtained by suspension. By focusing on methods in circle dynamics and linearization theorems, we give a sufficient condition to obtain a normal form as a…
We present a Phragm\'en-Lindel\"of type theorem with a flavor of Nevanlinna's theorem for subharmonic functions with frequent oscillations between zero and one. We use a technique inspired by a paper of Jones and Makarov.
We construct topological defects in the Liouville field theory producing jump in the value of cosmological constant. We construct them using the Cardy-Lewellen equation for the two-point function with defect. We show that there are…
The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…
We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.
We prove pfaffian and hafnian versions of Lieb's inequalities on determinants and permanents of positive semi-definite matrices. We use the hafnian inequality to improve the lower bound of R\'ev\'esz and Sarantopoulos on the norm of a…