**Contemporary Mathematics**

Volume: 665;
2016;
335 pp;
Softcover

MSC: Primary 46; 30; 32; 26; 47; 22; 37;

**Print ISBN: 978-1-4704-1988-2
Product Code: CONM/665**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

**Electronic ISBN: 978-1-4704-3204-1
Product Code: CONM/665.E**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

# Advances in Non-Archimedean Analysis

Share this page *Edited by *
*Helge Glöckner; Alain Escassut; Khodr Shamseddine*

This volume contains the Proceedings of the
13th International Conference on \(p\)-adic Functional
Analysis, held from August 12–16, 2014, at the University of
Paderborn, Paderborn, Germany.

The articles included in this book feature recent developments in
various areas of non-Archimedean analysis, non-Archimedean functional
analysis, representation theory, number theory, non-Archimedean
dynamical systems and applications.

Through a combination of new research articles and survey papers,
this book provides the reader with an overview of current developments
and techniques in non-Archimedean analysis as well as a broad
knowledge of some of the sub-areas of this exciting and
fast-developing research area.

#### Readership

Graduate students and research mathematicians interested in analysis in non-Archimedian domains.

# Table of Contents

## Advances in Non-Archimedean Analysis

- Cover Cover11
- Title page iii2
- Contents iii4
- Preface v6
- Obituary note vii8
- Compact self-adjoint operators on free Banach spaces of countable type 110
- Fundamental solutions of pseudodifferential equations associated with quadratic forms in even dimension 1928
- Spectral theory for finite rank perturbations of unbounded diagonal operators in non-Archimedean Hilbert space 2938
- 1. Introduction 2938
- 2. Some Classes of Bounded Linear Operators on 𝔼_{𝜔} 3039
- 3. Unbounded Linear Operators on 𝔼_{𝜔} 3039
- 4. Spectral Analysis for the Class of Operators 𝑇=𝐷+𝐾 3443
- 5. Spectral Analysis for the Class of Operators 𝑇=𝐷+𝐹 3544
- 6. Computation of 𝜎ₑ(𝐷) 3746
- 7. Main Result 3948
- References 3948

- Ultrametric continuous linear representations of the compact groups 𝑆𝐿(2,ℤ_{𝕡}) and 𝔾𝕃(2,ℤ_{𝕡}) 4150
- Survey on the 𝑝-adic Hayman conjecture 5766
- Invariant manifolds for finite-dimensional non-Archimedean dynamical systems 7382
- Introduction and statement of main results 7382
- 1. Preliminaries and notation 7887
- 2. Spectral interpretation of hyperbolicity 8190
- 3. Behaviour close to a fixed point 8392
- 4. When \boldmath𝑊ₐ^{\obs}(𝑓,𝑝) is not only immersed 8594
- 5. Dependence of \boldmath𝑎-stable manifolds on \boldmath𝑎>0 8695
- 6. Results for automorphisms of Lie groups 8796
- References 8998

- On non-Archimedean quantitative compactness theorems 91100
- Large linear spaces of invertible operators on a Banach space 103112
- Applications of 𝑝-adic numbers: from physics to geology 121130
- An alternative proof of the non-Archimedean Montel theorem for polynomial dynamics 133142
- New identities and congruences for Euler numbers. 139148
- On some transcendental values of the 𝑝-adic gamma function 159168
- The implicit function theorem on a field 𝐾 with an infinite rank valuation 165174
- Fractional differentiability and unitarity on parabolic inductions 177186
- Introduction 178187
- Part 0. Terminology 179188
- Part 1. The open cell as a representation of P 182191
- Part 2. Locally polynomial differentiable functions 185194
- Part 3. Construction of the greatest unitary norm on the open cell 190199
- Wim Schikhof: our colleague and friend 199208
- Solvability of rank one 𝑝-adic differential and 𝑞-difference equations over the Amice ring 251260
- Introduction 251260
- Introduction 251260
- First part : solvability of rank one differential equations over ℰ_{𝒦} 252261
- First part : solvability of rank one differential equations over ℰ_{𝒦} 252261
- 1. Notations 252261
- 2. Criterion of solvability for differential equations over ℰ_{𝒦} 255264
- Second part : solvability of rank one 𝑞-difference equations over ℰ_{𝒦} 262271
- Second part : solvability of rank one 𝑞-difference equations over ℰ_{𝒦} 262271
- 3. Some numerical Lemmas 262271
- 4. The Motzkin decomposition 264273
- 5. Criterion of solvability for 𝑞-difference equations over ℰ_{𝒦} 266275
- References 276285

- A note on Banach spaces over a rank 1 discretely valued field 279288
- Measure theory and Lebesgue-like integration in two and three dimensions over the Levi-Civita field 289298
- On complemented subspaces of non-Archimedean generalized power series spaces 327336
- Back Cover Back Cover1346