8 citations · 26 across the 12 of their papers we have counts for
14 papers
Decay of Fourier transforms and analytic continuation of power-constructible functions
Georges Comte, Dan J. Miller, Tamara Servi
For a subfield K of C, we denote by C^K the category of algebras of functions defined on the globally subanalytic sets that are generated by all K-powers and logarithms of positive…
Analytic holonomicity of real C-class distributions
Avraham Aizenbud, Raf Cluckers, Michel Raibaut +1
We introduce a notion of distributions on , called distributions of C-class, based on wavelet transforms of distributions and the theory from Clucker…
Transasymptotic expansions of o-minimal germs
Jean-Philippe Rolin, Tamara Servi, Patrick Speissegger
Given an o-minimal expansion of the real ordered field, generated by a generalized quasianalytic class , we construct an explicit truncation…
Parametric Fourier and Mellin transforms of power-constructible functions
Raf Cluckers, Georges Comte, Tamara Servi
We enrich the class of power-constructible functions, introduced in [CCRS23], to a class of algebras of functions which contains all complex powers of subanalytic functions, their…
Mellin transforms of power-constructible functions
Raf Cluckers, Georges Comte, Jean-Philippe Rolin +1
We consider several systems of algebras of real- and complex-valued functions, which appear in o-minimal geometry and related geometrically tame contexts. For each such system, we…
Multisummability for generalized power series
Jean-Philippe Rolin, Tamara Servi, Patrick Speissegger
We develop multisummability, in the positive real direction, for generalized power series with natural support, and we prove o-minimality of the expansion of the real field by all…
Linearization of complex hyperbolic Dulac germs
Dino Peran, Maja Resman, Jean-Philippe Rolin +1
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a compl…
Normal forms of hyperbolic logarithmic transseries
Dino Peran, Maja Resman, Jean-Philippe Rolin +1
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient conditi…
On local definability of holomorphic functions
Gareth Jones, Jonathan Kirby, Olivier Le Gal +1
Given a collection A of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from A. The notion of local definability of holomorphic f…
Integration of Oscillatory and Subanalytic Functions
Raf Cluckers, Georges Comte, Daniel J. Miller +2
We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials.…
Local interdefinability of Weierstrass elliptic functions
Gareth Jones, Jonathan Kirby, Tamara Servi
We explain which Weierstrass elliptic functions are locally definable from other elliptic functions and exponentiation in the context of o-minimal structures. The proofs make use o…
Multivariable Newton-Puiseux Theorem for Generalised Quasianalytic Classes
Tamara Servi
We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. Examples of the classes under consideration are the col…
Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras
Jean-Philippe Rolin, Tamara Servi
An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents.…
Definably complete and Baire structures and Pfaffian closure
Antongiulio Fornasiero, Tamara Servi
We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not be written as the…