相关论文: Two analytic continuations of the Lippmann-Schwing…
We provide a summary of the continuity properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator…
The analytic properties of automorphic L-functions have historically been obtained either through integral representations (the "Rankin-Selberg method"), or properties of the Fourier expansions of Eisenstein series (the "Langlands-Shahidi…
We give two distinct infinite-Hamiltonian representations for the Riemann equation. One with first order Hamiltonian operators and another with third order-first order Hamiltonian operators. Both representations contain an arbitrary…
We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…
We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…
The analytic Langlands correspondence proposed by Etingof, Frenkel and Kazhdan describes the solution to the spectral problems naturally arising in the quantisation of the Hitchin integrable systems in terms of real opers, certain second…
For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is…
The generating series of a number of different objects studied in arithmetic statistics can be built out of Euler products. Euler products often have very nice analytic properties, and by constructing a meromorphic continuation one can use…
A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds…
We extend recent results of Guan and Spruck, proving existence results for constant Gaussian curvature hypersurfaces in Hadamard manifolds.
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
We discuss the construction of higher-dimensional surfaces based on the harmonic maps of $S^2$ into $CP^{N-1}$ and other grassmannians. We show that there are two ways of implementing this procedure - both based on the use of the relevant…
Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives…
In this paper, using similar symbolical method of Burchnall and Chaundy formulas of expansion for the generalized hypergeometric function were constructed. By means of the found formulas of expansion the formulas of an analytic continuation…
In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a…
We prove decay estimates for generalized eigenfunctions of discrete Schr\"odinger operators on weighted infinite graphs in the spirit of Agmon.
We obtain the precise form of two Gamow functionals, representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing…
We review some topics in the analytic theory of Eisenstein series, including meromorphic continuation, $L^2$-spectral expansion and Fourier coefficients. We also discuss some open problems.
It is shown that the general 3-point function $<\Phi_{a} \Phi_{b} \Phi_{c}>$, with continuous values of charges $a, b, c$ of a statistical model operators, and the 3-point function of the Liouville model, could all be obtained by successive…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite…