Exponential forms and path integrals for complex numbers in dimensions.
Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact
We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations
In this paper, we study a class of first order nonlinear degenerate partial differential equations with singularity at . Using exponential-type Nagumo norm approach, the Gevrey asymptotic analysis is extended to case of holomorphic parameters in a natural way. A sharp condition is then established to deduce the -summability of the formal solutions. Furthermore, analytical solutions in conical domains are found for each type of these nonlinear singular PDEs.
Exposed points in the set of representing measures for the disc algebra
It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.
Extending analyticK-subanalytic functions
Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.
Extension a la dimension n d'un théorème de Ortel et Schneider.
Extension and normality of meromorphic mappings into complex projective varieties
The purpose of this article is twofold. The first is to show a criterion for the normality of holomorphic mappings into Abelian varieties; an extension theorem for such mappings is also given. The second is to study the convergence of meromorphic mappings into complex projective varieties. We introduce the concept of d-convergence and give a criterion of d-normality of families of meromorphic mappings.
Extension des Fonctions Plurisousharmoniques a Travers de "Petits" Sous-Ensembles
Extension du théorème de Cauchy aux fonctions d’une variable complexe de la forme
Extension Gevrey et rigidité dans un secteur
We study a rigidity property, at the vertex of some plane sector, for Gevrey classes of holomorphic functions in the sector. For this purpose, we prove a linear continuous version of Borel-Ritt's theorem with Gevrey conditions
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension of bilipschitz maps of compact polyhedra.
Extension of internally bilipschitz maps in John disks.
Extension of Zhu's solution to Lotto's conjecture on the weighted Bergman spaces.
Extension theorem for complex Clifford algebras-valued functions on fractal domains.
Extensions of Hiong's inequality.
Extensions of holomorphic motions
Extention of Apolarity and Grace Theorem
MSC 2010: 30C10The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of several well-known results...
Extrait d'une lettre à M. Hermite