Results 231 to 240 of about 79,736 (260)

Multivariable Calculus of Real Analytic Functions

2002
Definition 2.1.1 Set ℤ+ = {0, 1,2, . . .}. A multiindex μ is an element of (ℤ+) m ; we will write $$\Lambda (m) = (\mathbb{Z}^ + )^m ,$$ but often the size m of a multiindex will be understood from the context.
Steven G. Krantz, Harold R. Parks
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Hyperseries and generalized real analytic functions

2023
The main goal of this PhD thesis has been to start developing the theory of generalized real analytic functions (GRAF). The framework is that of generalized smooth functions, a branch of Colombeau theory where generalized functions share many nonlinear properties with ordinary smooth functions, like the closure with respect to composition, a good ...
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Composition operators on spaces of real analytic functions

Mathematische Nachrichten, 2003
AbstractLet Ω1, Ω2be open subsets of ℝand ℝ, respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operatorCφ: A(Ω1) → A(Ω2),Cφ(f) ≔f∘φ, is a topological embedding.
Domański, Paweł, Langenbruch, Michael
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Analytic, Real Analytic and Harmonic Generalized Functions

Sarajevo Journal of Mathematics
We recall definitions and assertions concerning the spaces noted in the title. Various classes of nonlinear problems can be studied within these spaces appropriate for the analysis of different kinds of singularities. Especially, we explain in this paper the notion of the generalized analytic wave front set.   2000 Mathematics Subject Classification.
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A division theorem for real analytic functions

Bulletin of the London Mathematical Society, 2007
AbstractWe characterize those homogeneous polynomials P e ℂ[z 1 , … , z d ] for which the principal ideal (P) = P · A(ℝ d ) is complemented in A(ℝ d ) or, equivalently, those which admit a continuous linear division operator. The condition is the same as that which characterizes, among the homogeneous polynomials, those which are nonelliptic and for ...
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Satisfiability of Systems of Equations of Real Analytic Functions Is Quasi-decidable

2011
In this paper we consider the problem of checking whether a system of equations of real analytic functions is satisfiable, that is, whether it has a solution. We prove that there is an algorithm (possibly non-terminating) for this problem such that (1) whenever it terminates, it computes a correct answer, and (2) it always terminates when the input is ...
Franek, P. (Peter), Ratschan, S. (Stefan), Zgliczynski, P.   +2 more
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Elliptic partial differential equationsfor real analytic functions

Mathematische Zeitschrift, 2000
The problem of existence of a continuous linear right inverse operator for a given partial differential operators is studied. Suppose \(K\subset\mathbb{R}^N\) is a compact convex set with nonempty interior, \(\partial K\) is the boundary of \(K,\) \(A(K)\) is the space of all real analytic functions on \(K\) and the partial differential operator \(P(D):
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Real Analytic Functions on Product Spaces and Separate Analyticity

Canadian Journal of Mathematics, 1961
Let f be a function on the product space V × W, where V and W are analytic manifolds, both either real or complex. The function f is said to be analytic (or bi-analytic) on V × W if it is analytic in the analytic structure induced on V × W by the corresponding structures on V and W. The function f is said to be separately analytic on V × W if, for each
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The Bochner—Martinelli integral operator for real analytic functions

Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
Let D be a bounded domain in Cn (n > 1) with a real analytic connected boundary dD = Г. The Bochner-Martinelli integral (integral operator) M(f) is considered for real analytic functions f о n Г. It is shown th at the integral M (f) is real analytic up to Г. Iterations of the Bochner-Martinelli integral Mk(f) are considered.
A. M. Kytmanov, S. G. Myslivets
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Real Analytic Functions as Ratios of Absolutely Monotonic Functions

1973
The problem we consider here is under what conditions analytic functions which are positive on a segment of the real axis can be expressed as ratios of two absolutely monotonic functions, that is, functions all of whose derivatives are non-negative on the given segment.
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