ترغب بنشر مسار تعليمي؟ اضغط هنا

Global approximation of CR functions on Bloom-Graham model graphs in $C^n$

345   0   0.0 ( 0 )
 نشر من قبل Daniel Jupiter
 تاريخ النشر 2004
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We define a class of generic CR submanifolds of $C^n$ of real codimension $d$, with $d$ in $1, ..., n-1$, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem, for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.


قيم البحث

اقرأ أيضاً

In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pluriharmonic boundary values. In the second scenario the structures are related by projective duality considerations. In both cases we provide explicit vector field-based characterizations for two-dimensional circular domains satisfying natural convexity conditions.
A smooth, strongly $mathbb{C}$-convex, real hypersurface $S$ in $mathbb{CP}^n$ admits a projective dual CR structure in addition to the standard CR structure. Given a smooth function $u$ on $S$, we provide characterizations for when $u$ can be decomp osed as a sum of a CR function and a dual CR function. Following work of Lee on pluriharmonic boundary values, we provide a characterization using differential forms. We further provide a characterization using tangential vector fields in the style of Audibert and Bedford.
This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly J-plurisubharmonic exhaustion f unction. Let u be an (upper semi-continuous) J-plurisubharmonic function on X. Then there exists a sequence {u_j} of smooth, strictly J-plurisubharmonic functions point-wise decreasing down to u. On any almost complex manifold (X,J) each point has a fundamental neighborhood system of J-pseudoconvex domains, and so the theorem above establishes local smooth approximation on X. This result was proved in complex dimension 2 by the third author, who also showed that the result would hold in general dimensions if a parallel result for continuous approximation were known. This paper establishes the required step by solving the obstacle problem.
We compute the exact norms of the Leray transforms for a family $mathcal{S}_{beta}$ of unbounded hypersurfaces in two complex dimensions. The $mathcal{S}_{beta}$ generalize the Heisenberg group, and provide local projective approximations to any smoo th, strongly $mathbb{C}$-convex hypersurface $mathcal{S}_{beta}$ to two orders of tangency. This work is then examined in the context of projective dual $CR$-structures and the corresponding pair of canonical dual Hardy spaces associated to $mathcal{S}_{beta}$, leading to a universal description of the Leray transform and a factorization of the transform through orthogonal projection onto the conjugate dual Hardy space.
In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investi gate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا