The Seventh International Conference on p-adic Functional Analysis was held
at the University of Nijmegen, The Netherlands, June 17-21, 2002. This conference
series began in Laredo, Spain (1990) and has continued with meetings every two
years in various places.
About 35 researchers from 15 different countries attended the June 2002 confer-
ence. This book contains research articles based on 30-minute talks given at the con-
ference. The main topic was how the influence of functional analysis has extended
beyond real or complex numbers into many other areas such as non-Archimedean
valued fields. Based on the growing influence of functional analysis on other dis-
ciplines, we have included, for the first time, three survey papers that address
timely and important areas in functional analysis: p-adic meromorphic functions
("Uniqueness Problems and Applications of the Ultrametric Nevanlinna Theory"),
nonclassical Hilbert spaces ("Hilbert-Like Spaces over Krull Valued Fields"), and p-
adic locally convex spaces ("Locally Convex Spaces over Non-Archimedean Valued
Basic functional analysis is represented by contributions covering a wide range
of topics: Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive
limits, spaces of continuous functions, strict topologies, operator theory, automatic
continuity, measure and integration, Banach and topological algebras, summabil-
ity methods, and ultrametric spaces. Analytic functions-meromorphic functions,
roots of rational functions, characterization of injective holomorphic functions, and
Gelfand transforms in algebras of analytic functions-are the subject of several pa-
pers. In addition the reader will find studies on differential equations, Banach Hopf-
algebras, Cauchy theory on Levi-Civita fields, finite differences, weighted means,
p-adic dynamical systems, and non-archimedean probability theory and stochastic
We are grateful to the University of Nijmegen's analysis group, the Mathemati-
cal Research Institute (MRI), the Netherlands Organization for Scientific Research
(NWO), and the Royal Dutch Academy of Sciences (KNAW) for their financial
support. We wish to thank the American Mathematical Society for publishing this
W. H. Schikhof
C. Perez-Garcia
A. Escassut
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