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Fournier, Richard

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Adjunct Professor

Faculty of Arts and Science - Department of Mathematics and Statistics

André-Aisenstadt

514 343-6111 ext 2714

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Research area

Student supervision Expand all Collapse all

Universal numerical series Theses and supervised dissertations / 2023-12
Borochof, Gabriel
Abstract
This master's thesis will be centered around the subject of universality in complex analysis. First, we will provide a summary of many of the results that have been discovered in the field of universality. We will show that, in most cases, the proofs of existence of the universal elements are not constructive, but, rather, implicit. We will perform an in-depth analysis of a specific proof of the existence of Universal Taylor series which was intended to be constructive and we will determine whether or not this goal was achieved. To do this, we will introduce a new universal element, which we will call Universal numerical series. These are complex numerical series such that the partial sums of the series are dense in the complex plane. We will give a constructive proof of the existence of these elements and, in order to fully determine whether the aforementioned proof of the existence of the Universal Taylor series is constructive, we will compare it to our proof of the existence of the Universal numerical series. Finally, we will examine the topological and algebraic properties of the Universal numerical series, showing under which conditions they are topologically generic and algebraically generic in the set of all complex numerical series.

Link to the Papyrus's document

Universalité, variables complexes et réarrangement Theses and supervised dissertations / 2011-02
Giguêre, Jérôme-Melville
Abstract
This Master’s thesis mainly concerns universality in complex analysis. First, we shall summarize general results on universal series and on a new type of universality introduced by Fournier and Nestoridis. Then, we shall introduce a new kind of universal series which are obtained by rearranging terms of arbitrary series. We will prove the algebraic genericity of these series for any Banach space and the topological genericity for finite dimensional spaces. Also, we will demonstrate that for any universal series in this sense, there exists a rearrangement of its terms for which it becomes universal in the usual sense.

Link to the Papyrus's document

Sur l'inégalité de Visser Theses and supervised dissertations / 2009-12
Zitouni, Foued
Abstract
Let p be a polynomial in the variable z. There exist several inequalities between the coefficents of p and its maximum modulus. In this work, we shall mainly study known proofs of the Visser inquality together with some extensions. We shall finally apply the inequality of Visser to obtain extensions of the Chebyshev inequality.

Link to the Papyrus's document

Les inégalités de Bernstein Theses and supervised dissertations / 2006
Lesage, Frédéric
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

À propos du Lemme de Jack Theses and supervised dissertations / 2006
Serban, Marius
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

Sur la conjecture de Bieberbach Theses and supervised dissertations / 2005
Rémillard, Alain
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

Le théorème de Bloch sur le recouvrement holomorphe Theses and supervised dissertations / 2002
Ayoub, Nabil
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

Les espaces Hp et leurs duaux Theses and supervised dissertations / 2001
Rathé, Pierre-Olivier
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Link to the Papyrus's document

Selected publications Expand all Collapse all

A new class of inequalities for polynomials

Fournier, Richard, A new class of inequalities for polynomials 44, 1171--1181 (2014), , Rocky Mountain J. Math.

Bound-preserving operators and the maximum modulus of extremal polynomials

Fournier, Richard, Bound-preserving operators and the maximum modulus of extremal polynomials 14, 735--741 (2014), , Comput. Methods Funct. Theory

Discrete Bernstein inequalities for polynomials

Fournier, Richard, Discrete Bernstein inequalities for polynomials 17, 241--248 (2014), , Math. Inequal. Appl.

Jack's lemma and a class of polynomial inequalities

Fournier, Richard, Jack's lemma and a class of polynomial inequalities 55(78), 172--177 (2013), , Mathematica

A note on an interpolation formula

Fournier, Richard, A note on an interpolation formula Fournier, Richard, Art. ID 00028, 5 (2013), , J. Interpolat. Approx. Sci. Comput.

On a discrete norm for polynomials

Fournier, R., Ruscheweyh, S. et Salinas C., L., On a discrete norm for polynomials 396, 425--433 (2012), , J. Math. Anal. Appl.

Non-normal sequences of holomorphic functions and universality

Fournier, Richard et Nestoridis, Vassili, Non-normal sequences of holomorphic functions and universality 11, 309--316 (2011), , Comput. Methods Funct. Theory

Estimates for the uniform norm of complex polynomials in the unit disk

Fournier, Richard, Letac, Gérard et Ruscheweyh, Stephan, Estimates for the uniform norm of complex polynomials in the unit disk 283, 193--199 (2010), , Math. Nachr.

Equality cases for two polynomial inequalities

Dryanov, D. et Fournier, R., Equality cases for two polynomial inequalities 99, 169--181 (2009), , Annuaire Univ. Sofia Fac. Math. Inform.

Refinement of an inequality of P. L. Chebyshev

Dryanov, D. et Fournier, R., Refinement of an inequality of P. L. Chebyshev 122, 59--69 (2009), , Acta Math. Hungar.

On a polynomial inequality

Fournier, Richard, On a polynomial inequality 351, 163--169 (2009), , J. Math. Anal. Appl.

Asymptotics of the Bohr radius for polynomials of fixed degree

Fournier, Richard, Asymptotics of the Bohr radius for polynomials of fixed degree 338, 1100--1107 (2008), , J. Math. Anal. Appl.

On a differential inequality

Fournier, Richard, On a differential inequality 28, 313--318 (2008), , Analysis (Munich)

An extension of Jack's lemma to polynomials of fixed degree

Fournier, Richard et Serban, Marius, An extension of Jack's lemma to polynomials of fixed degree 7, 371--378 (2007), , Comput. Methods Funct. Theory

Some extensions of the Markov inequality for polynomials

Dryanov, D., Fournier, R. et Ruscheweyh, S., Some extensions of the Markov inequality for polynomials 37, 1155--1165 (2007), , Rocky Mountain J. Math.

A class of locally univalent functions defined by a differential inequality

Fournier, R. et Ponnusamy, S., A class of locally univalent functions defined by a differential inequality 52, 1--8 (2007), , Complex Var. Elliptic Equ.

Cases of equality for refinements of Bernstein's inequality

Fournier, Richard et Lesage, Frédéric, Cases of equality for refinements of Bernstein's inequality 6, 51--58 (2006), , Comput. Methods Funct. Theory

On an improvement of Bernstein's polynomial inequalities

Dryanov, Dimiter et Fournier, Richard, On an improvement of Bernstein's polynomial inequalities 9, 343--349 (2006), , Math. Inequal. Appl.

A note on Bernstein and Markov type inequalities

Dryanov, D. et Fournier, R., A note on Bernstein and Markov type inequalities 136, 84--90 (2005), , J. Approx. Theory

On a discrete variant of Bernstein's polynomial inequality

Dryanov, Dimiter et Fournier, Richard, On a discrete variant of Bernstein's polynomial inequality 25, 73--77 (2005), , Analysis (Munich)

Cases of equality for a class of bound-preserving operators over ${\scr P}_n$

Fournier, Richard, Cases of equality for a class of bound-preserving operators over ${\scr P}_n$ 4, 183--188 (2004), , Comput. Methods Funct. Theory

Walter Hengartner, 1936--2003 [Dedicated to the memory of Walter Hengartner]

Bshouty, D. et Fournier, R., Walter Hengartner, 1936--2003 [Dedicated to the memory of Walter Hengartner] 4, i--ix (2004), , Comput. Methods Funct. Theory

On nonvanishing solutions of a class of functional equations

Fournier, Richard, On nonvanishing solutions of a class of functional equations 33, 1313--1322 (2003), , Rocky Mountain J. Math.

Differential inequalities and starlikeness

Fournier, Richard et Mocanu, Petru, Differential inequalities and starlikeness 48, 283--292 (2003), , Complex Var. Theory Appl.

Bound-preserving operators and Bernstein type inequalities

Dryanov, Dimiter et Fournier, Richard, Bound-preserving operators and Bernstein type inequalities 2, 397--414 (2002), , Comput. Methods Funct. Theory

Bound preserving operators over classes of polynomials

Dryanov, Dimiter et Fournier, Richard, Bound preserving operators over classes of polynomials 8, 327--353 (2002), , East J. Approx.

Some remarks on Jack's lemma

Fournier, Richard, Some remarks on Jack's lemma 43(66), 43--50 (2003) (2001), , Mathematica

A generalization of the Schwarz-Carathéodory reflection principle and spaces of pseudo-metrics

Fournier, Richard et Ruscheweyh, Stephan, A generalization of the Schwarz-Carathéodory reflection principle and spaces of pseudo-metrics 130, 353--364 (2001), , Math. Proc. Cambridge Philos. Soc.

Inequalities involving weighted means in a disc of the complex plane

Fournier, Richard, Inequalities involving weighted means in a disc of the complex plane 243, 313--325 (2000), , J. Math. Anal. Appl.

Extensions of the geometric-arithmetic means inequality to a disc of the complex plane

Fournier, Richard, Extensions of the geometric-arithmetic means inequality to a disc of the complex plane 2, 19--24 (1999), , Math. Inequal. Appl.

Free boundary value problems for analytic functions in the closed unit disk

Fournier, Richard et Ruscheweyh, Stephan, Free boundary value problems for analytic functions in the closed unit disk 127, 3287--3294 (1999), , Proc. Amer. Math. Soc.

On linear functionals of rational type over $H(\bold D)$

Fournier, Richard, On linear functionals of rational type over $H(\bold D)$ 173, 169--175 (1995), , Math. Nachr.

On two extremal problems related to univalent functions

Fournier, Richard et Ruscheweyh, Stephan, On two extremal problems related to univalent functions 24, 529--538 (1994), , Rocky Mountain J. Math.

Remarks on a multiplier conjecture for univalent functions

Fournier, Richard et Ruscheweyh, Stephan, Remarks on a multiplier conjecture for univalent functions 116, 35--43 (1992), , Proc. Amer. Math. Soc.

On generalized sections of univalent functions

Fournier, Richard et Silverman, Herb, On generalized sections of univalent functions 17, 141--147 (1992), , Complex Variables Theory Appl.

New inequalities for starlike univalent functions in the unit disc bounded on a diameter

Fournier, Richard, New inequalities for starlike univalent functions in the unit disc bounded on a diameter 39, 39--48 (1991), , Bull. Polish Acad. Sci. Math.

Radii problems for generalized sections of convex functions

Fournier, Richard et Silverman, Herb, Radii problems for generalized sections of convex functions 112, 101--107 (1991), , Proc. Amer. Math. Soc.

The range of a continuous linear functional over a class of functions defined by subordination

Fournier, Richard, The range of a continuous linear functional over a class of functions defined by subordination 32, 381--387 (1990), , Glasgow Math. J.

Starlike univalent functions bounded on the real axis

Fournier, Richard, Starlike univalent functions bounded on the real axis 41, 642--658 (1989), , Canad. J. Math.

On integrals of bounded analytic functions in the closed unit disc

Fournier, Richard, On integrals of bounded analytic functions in the closed unit disc 11, 125--133 (1989), , Complex Variables Theory Appl.

A growth theorem for a class of convex functions

Fournier, R., A growth theorem for a class of convex functions 40, 31--39 (1987) (1986), , Ann. Univ. Mariae Curie-Sk?odowska Sect. A

On neighbourhoods of univalent starlike functions

Fournier, Richard, On neighbourhoods of univalent starlike functions 47, 189--202 (1986), , Ann. Polon. Math.

On neighbourhoods of univalent convex functions

Fournier, Richard, On neighbourhoods of univalent convex functions 16, 579--589 (1986), , Rocky Mountain J. Math.

Some distortion theorems for a class of convex functions

Fournier, Richard, Some distortion theorems for a class of convex functions 15, 123--131 (1985), , Rocky Mountain J. Math.

A note on neighbourhoods of univalent functions

Fournier, Richard, A note on neighbourhoods of univalent functions 87, 117--120 (1983), , Proc. Amer. Math. Soc.

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