A counterexample to subanalyticity of an arc-analytic function
Krzysztof Kurdyka (1991)
Annales Polonici Mathematici
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We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.
Displaying similar documents to “An arc-analytic function with nondiscrete singular set”
A counterexample to subanalyticity of an arc-analytic function
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Isabelle Bonnard, Federica Pieroni (2004)
Revista Matemática Complutense
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We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper...
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Khan, Mumtaz Ahmad, Najmi, M. (2002)
Novi Sad Journal of Mathematics
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On the intersection product of analytic cycles
Sławomir Rams (2000)
Annales Polonici Mathematici
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We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).
Improper intersection of analytic curves.
Krasiński, Tadeusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Some properties of certain analytic functions.
Nishiwaki, Junichi, Owa, Shigeyoshi (2007)
Acta Universitatis Apulensis. Mathematics - Informatics
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Whitney stratification of sets definable in the structure
Ta Loi (1996)
Banach Center Publications
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The aim of this paper is to prove that every subset of definable from addition, multiplication and exponentiation admits a stratification satisfying Whitney’s conditions a) and b).
Analytic cell decomposition of sets definable in the structure
Ta Lê Loi (1994)
Annales Polonici Mathematici
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We prove that every set definable in the structure can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.
On a subordination result for analytic functions defined by convolution
E. A. Oyekan, T. O. Opoola (2014)
Annales UMCS, Mathematica
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In this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U
Analytic solutions of a first order functional differential equation with a state derivative dependent delay.
Zhang, Pingping (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Plurisubharmonic extension in non-degenerate analytic polyhedra.
Åhag, Per, Czyż, Rafał, Lodin, Sam, Wikström, Frank (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Intersection theory in complex analytic geometry
Piotr Tworzewski (1995)
Annales Polonici Mathematici
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We present a construction of an intersection product of arbitrary complex analytic cycles based on a pointwise defined intersection multiplicity.
Some applications of generalized condensers in the theory of analytic functions.
Dubinin, V.N., Èĭrikh, N.V. (2004)
Zapiski Nauchnykh Seminarov POMI
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On arc-analytic functions definable by a Weierstrass system
Krzysztof Jan Nowak (2011)
Annales Polonici Mathematici
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This paper presents certain characterizations through blowing up of arc-analytic functions definable by a convergent Weierstrass system closed under complexification.