In Example 1, we describe a subset X of the plane and a function on X which has a -extension to the whole for each finite, but has no -extension to . In Example 2, we construct a similar example of a subanalytic subset of ; much more sophisticated than the first one. The dimensions given here are smallest possible.
Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The θ-functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Bailey suggested the possibility of applying an analogue of Shimura's...
For a wedge of , we introduce two conditions of weak -pseudoconvexity, and prove that they entail solvability of the -system for forms of degree with coefficients in and respectively. Existence and regularity for in is treated by Hörmander [5, 6] (and also by Zampieri [9, 11] in case of piecewise smooth boundaries). Regularity in is treated by Henkin [4] (strong -pseudoconvexity by the method of the integral representation), Dufresnoy [3] (full pseudoconvexity), Michel [8] (constant...
If Ω is a domain of holomorphy in Cn, having a compact topological closure into another domain of holomorphy U ⊂ Cn such that (Ω,U) is a Runge pair, we construct a function F holomorphic in Ω which is singular at every boundary point of Ω and such that F is in Lp(Ω), for any p ∈ (0, +∞).
L’existence de solutions holomorphes locales d’équations aux dérivées partielles d’ordre infini à coefficients holomorphes de type spécial est étudiée.
We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) -dimensional symplectic manifolds endowed with a -tamed almost complex structure and with a nowhere vanishing and normalized section of the bundle satisfying the condition .We study the moduli space of QIS deformations of a given Calabi-Yau manifold, computing its tangent space and showing that is non obstructed. Finally, we present several examples of QIS manifolds.
Let f: ℝⁿ → ℝ be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Łojasiewicz’s gradient inequality states that there exist C > 0 and ϱ ∈ (0,1) such that in a neighbourhood of the origin. We prove that the smallest such exponent ϱ is not greater than with .
We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing t-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are equivalent to the former ones. In particular , we are able to realize perverse sheaves categories as non full abelian subcategories of the usual bounded complexes of sheaves categories. Our methods use induction on perversities. In this paper, we restrict...