共查询到20条相似文献,搜索用时 0 毫秒
1.
The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann–Hilbert problems on compact Riemann
surfaces. A formula for the Cauchy kernel can be given as an infinite sum over the elements of a Schottky group, and this
sum is often used for the explicit evaluation of the kernel. In this paper a new formula for a quasi-automorphic analogue
of the Cauchy kernel in terms of the Schottky–Klein prime function of the associated Schottky double is derived. This formula
opens the door to finding new ways to evaluate the analogue of the Cauchy kernel in cases where the infinite sum over a Schottky
group is not absolutely convergent. Application of this result to the solution of the Riemann–Hilbert problem with a discontinuous
coefficient for symmetric automorphic functions is discussed.
Received: March 10, 2007. Accepted: April 11, 2007. 相似文献
2.
A regular extension phenomenon of functions defined on Euclidean space with values in a Clifford algebra was studied by Le
Hung Son in the 90’s using methods of Clifford analysis, a function theory which, is centred around the notion of a monogenic
function, i.e. a null solution of the firstorder, vector-valued Dirac operator in .
The isotonic Clifford analysis is a refinement of the latter, which arises for even dimension. As such it also may be regarded
as an elegant generalization to complex Clifford algebra-valued functions of both holomorphic functions of several complex
variables and two-sided biregular function theories.
The aim of this article is to present a Hartogs theorem on isotonic extendability of functions on a suitable domain of . As an application, the extension problem for holomorphic functions and so for the two-sided biregular ones is discussed.
相似文献
3.
Rubén A. Hidalgo 《Journal of Pure and Applied Algebra》2018,222(12):4173-4188
Let p be a prime integer and let be an integer so that . We show that a closed Riemann surface S of genus has at most one p-group H of conformal automorphisms so that has genus zero and exactly r cone points. This, in particular, asserts that, for and , the minimal field of definition of S coincides with that of . Another application of this fact, for the case that S is pseudo-real, is that must be either trivial or a cyclic group and that r is necessarily even. This generalizes a result due to Bujalance–Costa for the case of pseudo-real cyclic p-gonal Riemann surfaces. 相似文献
4.
C. -F. Bödigheimer 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2006,76(1):191-233
In this article we consider Riemann surfacesF of genus g ≥ 0 with n ≥ 1 incoming and m ≥ 1 outgoing boundary circles, where on each incoming circle a point is marked.
For the moduli space mg*(m, n) of all suchF of genusg ≥ 0 a configuration space model Radh(m, n) is described: it consists of configurations of h = 2g-2+m+n pairs of radial slits distributed over n annuli; certain combinatorial conditions must be satisfied to guarantee the genusg and exactly m outgoing circles. Our main result is a homeomorphism between Radh(m, n) and Mg*(m,n).
The space Radh(m, n) is a non-compact manifold, and the complement of a subcomplex in a finite cell complex. This can be used for homological
calculations. Furthermore, the family of spaces Radh(m, n ) form an operad, acting on various spaces connected to conformai field theories. 相似文献
5.
6.
We introduce the algebra of smoothing Mellin and Green symbols in a pseudodifferential calculus for manifolds with edges. In addition, we define scales of weighted Sobolev spaces with asymptotics based on the Mellin transform and analyze the mapping properties of the operators on these spaces. This will allow us to obtain complete information on the regularity and asymptotics of solutions to elliptic equations on these spaces. 相似文献
7.
We develop a constructive framework to define difference approximations of Dirac operators which factorize the discrete Laplacian.
This resulting notion of discrete monogenic functions is compared with the notion of discrete holomorphic functions on quad-graphs.
In the end Dirac operators on quad-graphs are constructed. 相似文献
8.
The main objective is the study of a class of boundary value problems in weak formulation where two boundary conditions are
given on the half-lines bordering the first quadrant that contain impedance data and oblique derivatives. The associated operators
are reduced by matricial coupling relations to certain boundary pseudodifferential operators which can be analyzed in detail.
Results are: Fredholm criteria, explicit construction of generalized inverses in Bessel potential spaces, eventually after
normalization, and regularity results. Particular interest is devoted to the impedance problem and to the oblique derivative
problem, as well. 相似文献
9.
Yoshihiko Yamaura 《Mediterranean Journal of Mathematics》2007,4(4):451-482
We construct a candidate of the gradient flow for a variational functional with a singular term in the one-dimensional case.
Applied is the scheme using the theory of Γ-convergence for variational functionals, where both the Dirichlet integral and
the singular term are approximated at the same time. An approximated solution is constructed on the space of piecewise constant
functions, and the desired gradient flow is built as the limit of it. We establish some properties of the gradient flow as
well as obtain PDE including a term of integration by Radon measure.
相似文献
10.
11.
M. Faierman R. J. Fries R. Mennicken M. Möller 《Integral Equations and Operator Theory》2000,38(1):9-27
We determine the essential spectrum of the linearized Navier-Stokes operator with physical boundary conditions. In contrast to other approaches we do not make use of pseudo-differential operators. We establish a direct proof using only some fundamental results for matrix operators.Supported in part by a grant from the NRF of South Africa and by the John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Johannesburg 相似文献
12.
The Bochner-Martinelli (B.-M.) kernel inherits, forn2, only some of properties of the Cauchy kernel in . For instance it is known that the singular B.-M. operatorM
n
is not an involution forn2. M. Shapiro and N. Vasilevski found a formula forM
2
2
using methods of quaternionic analysis which are essentially complex-twodimensional. The aim of this article is to present a formula forM
n
2
for anyn2. We use now Clifford Analysis but forn=2 our formula coincides, of course, with the above-mentioned one. 相似文献
13.
We study the Cauchy–Dirichlet problem for a second-order quasilinear parabolic stochastic differential equation (SPDE) in a domain with a zero order noise term driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Hölder classes with weights. 相似文献
14.
Janez Bernik 《Archiv der Mathematik》2007,88(6):481-490
Let K be an algebraically closed field of arbitrary characteristic and F < K a subfield. If
is an irreducible semigroup of matrices such that the spectra of all the elements of
are contained in F, then
is conjugate to a subsemigroup of M
n
(F).
Research supported in part by the Ministry of Higher Education, Science, and Technology of Slovenia.
Received: 6 April 2006 相似文献
15.
The mapping class group of a surface with one boundary component admits numerous interesting representations including a representation as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class group can be identified with the fundamental group of Riemann's moduli space, it is furthermore identified with a subgroup of the fundamental path groupoid upon choosing a basepoint. A combinatorial model for this, the mapping class groupoid, arises from the invariant cell decomposition of Teichmüller space, whose fundamental path groupoid is called the Ptolemy groupoid. It is natural to try to extend representations of the mapping class group to the mapping class groupoid, i.e., to construct a homomorphism from the mapping class groupoid to the same target that extends the given representations arising from various choices of basepoint.Among others, we extend both aforementioned representations to the groupoid level in this sense, where the symplectic representation is lifted both rationally and integrally. The techniques of proof include several algorithms involving fatgraphs and chord diagrams. The former extension is given by explicit formulae depending upon six essential cases, and the kernel and image of the groupoid representation are computed. Furthermore, this provides groupoid extensions of any representation of the mapping class group that factors through its action on the fundamental group of the surface including, for instance, the Magnus representation and representations on the moduli spaces of flat connections. 相似文献
16.
17.
A.B.J. Kuijlaars K.T.-R. McLaughlin W. Van Assche M. Vanlessen 《Advances in Mathematics》2004,188(2):337-398
We consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1−x)α(1+x)βh(x), with α,β>−1 and h real analytic and strictly positive on [−1,1]. We obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval [−1,1], for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials. We also deduce asymptotic behavior for the Hankel determinants and for the monic orthogonal polynomials on the interval [−1,1]. For the asymptotic analysis we use the steepest descent technique for Riemann-Hilbert problems developed by Deift and Zhou, and applied to orthogonal polynomials on the real line by Deift, Kriecherbauer, McLaughlin, Venakides, and Zhou. In the steepest descent method we will use the Szeg? function associated with the weight and for the local analysis around the endpoints ±1 we use Bessel functions of appropriate order, whereas Deift et al. use Airy functions. 相似文献
18.
Fumiharu Kato 《Mathematische Zeitschrift》2008,259(3):631-641
We give an explicit construction of a unitary Shimura surface that has Mumford’s fake projective plane as one of its connected
components. Moreover, as a byproduct of the construction, we show that Mumford’s fake projective place has a model defined
over the 7th cyclotomic field. 相似文献
19.
Yi-Hu Yang 《Calculus of Variations and Partial Differential Equations》2008,32(4):411-427
We apply the Dirichlet’s principle to a modified energy functional on Riemann surfaces to reprove the existence of harmonic
metrics with certain prescribed singularities due to Simpson, Sabbah and Biquard–Boalch, and hence of differentials with twisted
coefficients of the second and third kinds. As a by-product, this generalizes the classical theory of Abelian differentials
on a compact Riemann surface to the case of twisted coefficients. This also proposes a more natural approach for general existence
of harmonic metrics in the higher dimensional case.
The author supported partially by NSF of China (No. 10471105, 10771160). 相似文献
20.
Pavel Drábek Peter Takáč 《Calculus of Variations and Partial Differential Equations》2007,29(1):31-58
An improved Poincaré inequality and validity of the Palais-Smale condition are investigated for the energy functional on , 1 < p < ∞, where Ω is a bounded domain in , is a spectral (control) parameter, and is a given function, in Ω. Analysis is focused on the case λ = λ1, where −λ1 is the first eigenvalue of the Dirichlet p-Laplacian Δ
p
on , λ1 > 0, and on the “quadratization” of within an arbitrarily small cone in around the axis spanned by , where stands for the first eigenfunction of Δ
p
associated with −λ1. 相似文献