Research Explorer

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Researcher

Hans Vernaeve

Publications & Research Data

Awards & Distinctions

28 Results

2024

A Grothendieck topos of generalized functions I : basic theory

Paolo GiordanoMichael KunzingerHans Vernaeve

A1 Journal Article in DISSERTATIONES MATHEMATICAE

2021

Filter-dependent versions of the uniform boundedness principle

Ben De BondtHans Vernaeve

A1 Journal Article in JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Regularity of nonlinear generalized functions : a counterexample in the nonstandard setting

A2 Journal Article in EXAMPLES AND COUNTEREXAMPLES

2019

A nonlinear theory of infrahyperfunctions

Andreas DebrouwereHans VernaeveJasson Vindas Diaz

A1 Journal Article in KYOTO JOURNAL OF MATHEMATICS

2018

Contributions to the linear and non-linear theory of ultradistributions

Andreas DebrouwereHans VernaeveJasson Vindas Diaz

Optimal embeddings of ultradistributions into differential algebras

Andreas DebrouwereHans VernaeveJasson Vindas Diaz

A1 Journal Article in MONATSHEFTE FUR MATHEMATIK

2017

An application of internal objects to microlocal analysis in generalized function algebras

Bookchapter in Generalized functions and Fourier analysis

2016

Generalized functions on the closure of an open set : applications to uniqueness of some characteristic Cauchy problem

Victor DévouéeJean-André MartiHans VernaeveJasson Vindas Diaz

A2 Journal Article in NOVI SAD JOURNAL OF MATHEMATICS

Microlocal analysis in generalized function algebras based on generalized points and generalized directions

A1 Journal Article in MONATSHEFTE FUR MATHEMATIK

2015

Strongly internal sets and generalized smooth functions

Paolo GiordanoMichael KunzingerHans Vernaeve

A1 Journal Article in JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

2014

Asymptotic distribution of integers with certain prime factorizations

Hans VernaeveJasson Vindas DiazAndreas Weiermann

A1 Journal Article in JOURNAL OF NUMBER THEORY

Asymptotic ideals (ideals in the ring of Colombeau generalized constants with continuous parametrization)

A KhelifD ScarpalezosHans Vernaeve

A1 Journal Article in COMMUNICATIONS IN ALGEBRA

Topological properties of regular generalized function algebras

A1 Journal Article in MONATSHEFTE FUR MATHEMATIK

2012

Characterization of distributions having a value at a point in the sense of Robinson

Hans VernaeveJasson Vindas Diaz

A1 Journal Article in JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

2011

Hilbert C-modules: structural properties and applications to variational problems

Claudia GarettoHans Vernaeve

A1 Journal Article in TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Isomorphisms of algebras of generalized functions

A1 Journal Article in MONATSHEFTE FUR MATHEMATIK

Nonstandard principles for generalized functions

A1 Journal Article in JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

2010

Ideals in the ring of Colombeau generalized numbers

A1 Journal Article in COMMUNICATIONS IN ALGEBRA

Weak homogeneity in generalized function algebras

A1 Journal Article in MATHEMATISCHE NACHRICHTEN

2009

Pointwise characterizations in generalized function algebras

A1 Journal Article in Monatshefte für Mathematik

2008

Full algebra of generalized functions and non-standard asymptotic analysis

Todor TodorovHans Vernaeve

A2 Journal Article in Logic And Analysis

Group invariant Colombeau generalized functions

A1 Journal Article in MONATSHEFTE FUR MATHEMATIK

Homogeneity in generalized function algebras

Clemens HanelEberhard MayerhoferStevana PilipovicHans Vernaeve

A1 Journal Article in Journal of Mathematical Analysis and Applications

Internal sets and internal functions in Colombeau theory

M OberguggenbergerHans Vernaeve

A1 Journal Article in JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

The local structure of nonstandard representatives of distributions

A2 Journal Article in Portugaliae mathematica

2003

Embedding distributions in algebras of generalized functions with singularities

A1 Journal Article in MONATSHEFTE FUR MATHEMATIK

Optimal embeddings of distributions into algebras

A1 Journal Article in PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

2001

Asymptotics of differentiated Bernstein polynomials

Christian ImpensHans Vernaeve

A1 Journal Article in CONSTRUCTIVE APPROXIMATION