This volume contains papers based on lectures given at the 12th International
Conference on p-adic Functional Analysis which was held at the University of
Manitoba from July 2 to July 6, 2012. The conference followed the tradition of
eleven earlier meetings which took place in Laredo (Spain, 1990), Santiago (Chile,
1992), Clermont-Ferrand (France, 1994), Nijmegen (The Netherlands, 1996), Poz-
nan (Poland, 1998), Ioannina (Greece, 2000), Nijmegen (The Netherlands, 2002),
Clermont-Ferrand (France, 2004), Concepci´ on (Chile, 2006), East Lansing (USA,
2008), and Clermont-Ferrand (France, 2010).
The 2012 conference and its proceedings, published in this special volume of
Contemporary Mathematics, are dedicated to our colleagues who have retired since
our previous meeting in 2010: Professors Bertin Diarra, Alain Escassut, Athanasios
Katsaras, Hans Keller, and Herminia Ochsenius who have continuously enriched
this series of conferences and the related proceedings with their original research
and wise guidance. We wish them the best and we look forward to their continued
contributions in the future.
The articles included in this book feature recent developments in various ar-
eas of non-Archimedean Analysis: Branched values and zeros of the derivative of
a p-adic meromorphic function, partial fractional differentiability, morphisms be-
tween ultrametric Banach algebras of continuous functions and maximal ideals of
finite dimension, p-adic q-distributions, Grobman-Hartman theorems for diffeomor-
phisms of Banach spaces over valued fields, integral representations of continuous
linear maps on p-adic spaces of continuous functions, non-Archimedean operator
algebras, generalized Keller spaces over valued fields, proper multiplications on the
completion of a totally ordered abelian group, generalized power series spaces, and
measure theory on Levi-Civita fields. The book also includes four survey papers:
one paper on p-adic meromorphic functions sharing a small function (by Kamal
Boussaf, Alain Escassut and Jacqueline Ojeda), one on Banach spaces over fields
with an infinite rank valuation (by Herminia Ochsenius and Elena Olivos), one on
the Grothendieck approximation theory in non-Archimedean Functional Analysis
(by Cristina Perez-Garcia), and my paper on power series and analytic functions
on Levi-Civita fields.
For their guidance and help while organizing the conference and during the
refereeing process, I am very grateful to the members of the conference’s Scien-
tific Committee: Jos´ e Aguayo, Jesus Araujo, Gilles Christol, Bertin Diarra, Alain
Escassut, Athanasios Katsaras, Herminia Ochsenius, Cristina Perez-Garcia, and
Wim Schikhof. I am also grateful to the University of Manitoba and the Winnipeg
Institute for Theoretical Physics for their financial and logistical support for the
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