Summer Symposium in Real Analysis XXXIV
"The Buckeye Symposium"

The College of Wooster, Wooster, Ohio, JULY 13-17, 2010

January 12, 2010

The Thirty-Fourth Summer Symposium in Real Analysis (The Buckeye Symposium) was hosted by The College of Wooster July 13-17, 2010. The Editorial Board of the EXCHANGE wishes to express its gratitude to The College of Wooster for its gracious hospitality and to the conference director, Pamela Pierce, for her outstanding leadership in organizing and conducting this symposium. Furthermore, both Pamela and the Editorial Board sincerely thank The National Science Foundation. The Buckeye Symposium was supported in part by grant DMS-1011888 from the National Science Foundation. We also are indebted to The College of Wooster for their financial and administrative support of this conference.


In addition to the formal mathematical program, time was set aside for research collaboration and a problem session. Wednesday evening found many of the participants enjoying the Ohio Light Opera's production of John Philip Sousa's {\em El Capitain}. On Thursday afternoon, the symposium participants were treated to a delightfully informative tour of the Amish region near Wooster. At the traditional Friday evening banquet, Conference Director Pierce awarded the {\it ANDY}' to {\bf Marianna Csornyei}. Congratulations, Marianna!

The conference featured invited one-hour addresses by:


as well as twenty-nine contributed talks. Following the participant list is the program of the Symposium, and then the summaries of the talks. The editorial board of the EXCHANGE wishes to thank the speakers for preparing these summaries.


James Aduci, Ali Alikhani, Pieter Allart, Chanchal Kumar Basu, Jack Brown, Jane Brown, Svetlana Butler, Marc Carnovale, Bishweshwar Choudary, Marianna Csörnyei, Udayan Darji, Geraldo de Souza, Gerald Edgar, Michael Evans, Márcia Federson, David Freund, Paul, Humke, Corey Jones, Robert Kantrowitz, Jun Kawabe, Kiko Kawamura, Steven Krantz, Eddy Armand Kwessi, Tamas Matrai, Mark Mc Clure, Paul Musial, Kirill Naralenkov, Lenka Obadalová, Pamela Pierce, Eric Samansky, Grzegorz Sitiniewski, Jaroslav Smital, Sarah Sprague, Tatiana Sworowska, Pietr Sworowski V\'aclav Vlas\'ak, Daniel Waterman, Martina Zähle, Ondrjěj Zindulka.


Pictured above are the participants of the Thirty-fourth Summer Symposium in Real Analysis.

Clockwise from the top: An astonished Marianna Csörnyei receives this year's "Andy" from an equally ebullient Pam Pierce. Eddy Kwessi finds plenty of mathematics to photograph in Wooster, while Ondrjěj Zindulka accompanies himself singing his own rendition of Edgar Allen Poe's The Raven.


WEDNESDAY Morning Session (Chair - Paul Humke)

9:00      P. Pierce and P. Humke
                  Opening Remarks and Announcements

9:10      Carolyn Newton, Provost of The College of Wooster
                  Welcome to Wooster!

9:25       S. Krantz
                  Convexity in Real Analysis

10:45       M. McClure
                  Finite Type Iterated Function Systems: a Computational Perspective

11:10       C. Jones
                  The Golden Ana Set

11:35       E. Talvila
                  Convolutions With the Continuous Primitive Integral

WEDNESDAY Afternoon Session 1 (Chair - Erik Talvila)

13:10       K. Naralenkov
                  On Continuity and Compactness of Some Vector-Valued Integrals

13:55       L. Obadalova
                  Irregular Recurrence in Compact Metric Spaces

14:20       G. Edgar
                  Fractional Iteration of Series and Transseries

14:45       E. Samansky
                  Probability Measures on Shrinking Neighborhoods

WEDNESDAY Afternoon Session 2 (Chair - Ali Alikhani)

15:30       M. Zähle
                  Local and Global Curvatures of Self-Similar Sets

15:55       O. Zindulka
                  Are Functions with a Monotone Graph Smooth?

16:20       R. Vallin
                  Results for Slowly Oscillating Continuous Functions

16:20       P. Humke
                  Transference of Density May be Possible

THURSDAY Morning Session 1 (Chair - Mark McClure)

9:00      R. Kantrowitz
                  Banach Algebra Norms for Spaces of Functions of Generalized Bounded Variation

9:25       D. Waterman
                  Variations on Axer's Theorem

9:50       E. M. Bonotto
                  A Feynman-Kac Solution to a Random Impulsive Equation of Schrädinger Type

THURSDAY Morning Session 2 (Chair - Robert Vallin)

10:40      G. DeSouza
                  A New Characterization of the Lorentz Spaces L(p,1) for p>1 and Applications

11:05       E. A. Kwessi
                  Characterization of Lacunary Functions in Weighted Bergman Besov Lipschitz Spaces

11:30       J. Kawabe
                  New Smoothness Conditions on Riesz Spaces with Applications to Riesz Space-Valued Non-Additive Measures and Their Choquet Integrals

FRIDAY Morning Session 1 (Chair - Udayan Darji)

8:45       M. Csörnyei        
                  Lipschitz Mappings

10:05       C. K. Basu
                  Uniformization Subtopology and a Sort of Converse of A. H. Stone's Theorem

10:35       P. Sworowski
                  On Baire One* Approximately Continuous Functions

10:55       P. Allart
                  Where does Takagi's Continuous, Nowhere Differentiable Function Have an Infinite Derivative?

11:20       K. Kawamura
                  The Derivative of Lebesgue's Singular Function

FRIDAY Afternoon Session 2 (Chair - Ondřej Zindulka)

13:30       B. Choudhary        
                  A Natural Extension of the Henstock-Kurzweil Integral

13:55       M. Federson
                  Linear FDEs in the Frame of Generalized ODEs: a Justification for Using Kurzweil Equations

14:20       U. Darji
                  Chaos Among Self-Maps of the Cantor Space

14:45       P. Musial
                  The $L^r$ Variational Integral

FRIDAY Afternoon Session 3 (Chair - Paul Musial)

15:30       J. Smital        
                  Distributional Chaos After 16 years

15:55       J. Adduci
                  Basis Properties of the Eigensystem of a Perturbed Harmonic Oscillator

16:20       T. Sworowska
                  On Recovery of a Function from its Trigonometric Integral

16:45       M. Evans
                  Baire one, Gibson and Weakly Gibson Real Functions of Several Real Variables