912 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Nanjing UniversityCN78 papers
- Centre National de la Recherche ScientifiqueFR49 papers
- Pennsylvania State UniversityUS48 papers
- Xi'an Jiaotong UniversityCN43 papers
- Center for Astrophysics Harvard & SmithsonianUS41 papers
- National Laboratory of Solid State Microstructures39 papers
- Argonne National LaboratoryUS38 papers
- Goddard Space Flight CenterUS38 papers
- Johns Hopkins UniversityUS31 papers
- Collaborative Innovation Center of Advanced MicrostructuresCN29 papers
- Université Paris-SaclayFR28 papers
- Tel Aviv UniversityIL26 papers
25 papers · 1 filter
Bicomplex Hardy Classes of Solutions to Higher-Order Vekua Equations
William L. Blair
We extend representation formulas for functions in Hardy classes of solutions to higher-order iterated Vekua equations to Hardy classes of bicomplex-valued functions that solve a b…
The -problem on -domains
Debraj Chakrabarti, Phillip S. Harrington, Andrew Raich
Given a complex manifold containing a relatively compact domain, we give sufficient geometric conditions on the domain so that its -cohomology in degree (known…
The Schwarz boundary value problem for boundary values in the sense of distributions
William L. Blair
We construct solutions to the Schwarz boundary value problem on the unit disk and the upper half-plane when the boundary condition is with respect to boundary values in the sense o…
An atomic representation for Hardy classes of solutions to nonhomogeneous Cauchy-Riemann equations
William L. Blair
We develop a representation of the second kind for certain Hardy classes of solutions to nonhomogeneous Cauchy-Riemann equations and use it to show that boundary values in the sens…
Optimal approximants and orthogonal polynomials in several variables
Meredith Sargent, Alan Sola
We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable…
The -Neumann operator with the Sobolev norm of integer orders
Phillip Harrington, Bingyuan Liu
Let be a bounded pseudoconvex domain with smooth boundary. For each , we give a sufficient condition to estimate the -Neumann o…
Hartogs Domains and the Diederich Fornæss Index
Muhenned Abdulsahib, Phillip S. Harrington
We study a geometric property of the boundary on Hartogs domains which can be used to find upper and lower bounds for the Diederich-Fornæss Index. Using this, we are able to show t…
Interpolation and sampling sequences for mixed-norm spaces
Phuc K. Nguyen, Daniel H. Luecking
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance prop…
Some Properties of the Higher Spin Laplace Operator
Chao Ding, John Ryan
The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irred…
Zero sets of functions in the Nevanlinna class and the -equation on convex domains of general type in
Tran Vu Khanh, Andrew Raich
The purpose of this paper is to characterize the zero sets of holomorphic functions in the Nevanlinna class on a class of convex domains of infinite type in . Moreove…
On Some Conformally Invariant Operators in Euclidean Space
Chao Ding, John Ryan
The aim of this paper is to correct a mistake in earlier work on the conformal invariance of Rarita-Schwinger operators and use the method of correction to develop properties of so…
The Szegö kernel on a class of noncompact CR manifolds of high codimension
Andrew Raich, Michael Tinker
We generalize Nagel's formula for the Szegö kernel and use it to compute the Szegö kernel on a class of noncompact CR manifolds whose tangent space decomposes into one complex dire…
Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type
Tran Vu Khanh, Andrew Raich
The purpose of this paper is to prove that if a pseudoconvex domains satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman pro…
Cauchy-type integrals in several complex variables
Loredana Lanzani, Elias M. Stein
We present the theory of Cauchy-Fantappié integral operators, with emphasis on the situation when the domain of integration, , has minimal boundary regularity. Among these opera…
The Kerzman-Stein operator for piecewise continuously differentiable regions
Michael Bolt, Andrew Raich
The Kerzman-Stein operator is the skew-hermitian part of the Cauchy operator defined with respect to an unweighted hermitian inner product on a rectifiable curve. If the curve is c…
Some Operators Associated to Rarita-Schwinger Type Operators
Junxia Li, John Ryan
In this paper we study some operators associated to the Rarita-Schwinger operators. They arise from the difference between the Dirac operator and the Rarita-Schwinger operators. Th…
Heat Kernels, Smoothness Estimates and Exponential Decay
Albert Boggess, Andrew Raich
In this article, we establish Gaussian decay for the Box_b-heat kernel on polynomial models in C^2. Our technique attains the exponential decay via a partial Fourier transform. On…
Regularity results for on CR-manifolds of hypersurface type
Phillip Harrington, Andrew Raich
We introduce a class of embedded CR manifolds satisfying a geometric condition that we call weak . For such manifolds, we show that dbar-b has closed range on and that…
Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type
Andrew Raich
The purpose of this article is to study compactness of the complex Green operator on CR manifolds of hypersurface type. We introduce (CR-P_q), a potential theoretic condition on $(…
-Dirac Operators
Craig A. Nolder, John Ryan
We introduce non-linear Dirac operators in associated to the -harmonic equation and we extend to other contexts including spin manifolds and the sphere.
An isoperimetric inequality for logarithmic capacity of polygons
Alexander Yu. Solynin, Victor A Zalgaller
We verify an old conjecture of G. Polya and G. Szego saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.
On the number of zeros of certain rational harmonic functions
Dmitry Khavinson, Genevra Neumann
Extending a result from the paper of D. Khavinson and G. Swiatek, we show that the rational harmonic function , where r(z) is a rational function of degree n > 1, h…
Introductory Clifford Analysis
John Ryan
This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction…
Vita: Friedrich Wilhelm Wiener
Harold P. Boas, Dmitry Khavinson
We report on the life and work of F. Wiener, whom we confused with N. Wiener in a previous article.