Inhalt

•  
  Fractional non-Archimedean calculus
•  
   Introduction
•  
   Prerequisites
•  
  Apparatus
•  
   Locally convex K-vector spaces
•  
  C-functions for [0,1[
•  
   Definition of C-functions
•  
   Properties of the space of C-functions
•  
   The locally convex topology on C-functions
•  
   Componentwise criteria for being C
•  
   C-.4-functions for -.4 [0,1[d
•  
   Definition of C-.4-functions
•  
   Properties of the space of C-.4-functions
•  
   C1+-functions
•  
  Fractional differentiability in one variable
•  
  Cr-functions for r R0
•  
   Definition of Cr-functions
•  
   Properties of Cr-functions
•  
   The locally convex K-algebra of Cr-functions
•  
   Description through iterated difference quotients
•  
  Characterization through Taylor polynomials
•  
   The Taylor polynomial of Cr-functions
•  
   Characterizing Cr-functions through Taylor polynomials on general domains
•  
   Sufficiency of the Taylor polynomial expansion on B-sets for Cr-functions
•  
   Another characterization of Cr-functions on compact sets and an application
•  
   Orthogonal bases on Zp
•  
   The van der Put base of C(Zp,K)
•  
   The Mahler base of C(Zp,K)
•  
   The Mahler Base of Cr(Zp,K)
•  
  Fractional differentiability in many variables
•  
  Cr-functions for r R0
•  
   Definition of Cr-functions
•  
   Properties of Cr-functions
•  
   The locally convex K-algebra of Cr-functions
•  
   Locally analytic functions in Cr(X,K) on an open domain
•  
   Composition properties of Cr-functions
•  
   Density of (locally) polynomial functions in Cr(X,K)
•  
  Orthogonal bases of Cr-functions on a compact domain
•  
   Interlude: Orthogonal bases of K-Banach spaces
•  
   The initial K-Banach algebra Cr(X,K) of thought topological tensor products Cr-.4(X,K) for r-.4 Nd=r
•  
   The Mahler base of Cr(Zpd,K)
•  
   Description of Cr(X,K) for open X Qpd through Taylor polynomials
•  
   The space Dr(X,K) of distributions on Cr(X,E) for a compact group X
•  
  Applications
•  
   Example of an induced Cr-representation
•  
   Cr-manifolds
•  
   References
•  
  The intertwined open cells in the universal unitary lattice of an unramified algebraic principal series
•  
   Introduction
•  
  Prerequisites
•  
   The groups
•  
   The representations
•  
   The universal unitary completion of a locally algebraic representation
•  
   The unramified dominant principal series as a representation of P
•  
  The universal unitary lattice of the P-representation on an open cell and a norm of differentiable functions
•  
   Interlude: The dominant submonoid acting on the affine root factors
•  
   The necessity criterion
•  
   The smooth case
•  
   Example: The smooth case of small order image
•  
   Example: The smooth split case
•  
   Interlude: Locally polynomial differentiable functions
•  
   The locally algebraic case
•  
  The universal unitary lattice of an unramified dominant principal series
•  
   The universal unitary lattice of the underlying P-representation
•  
   The Jacquet module
•  
   Gluing the universal unitary lattice from the intertwined open cells
•  
   References