scholarly journals A p-adic analytic family of the D-th Shintani lifting for a Coleman family and congruences between the central L-values

2017 ◽  
Vol 181 ◽  
pp. 164-199
Author(s):  
Kenji Makiyama
Keyword(s):  
Analytic Family

scholarly journals ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION

2020 ◽  
pp. 1-32
Author(s):  
Jesús M. F. Castillo ◽  
Willian H. G. Corrêa ◽  
Valentin Ferenczi ◽  
Manuel González
Keyword(s):  
Unit Circle ◽  
Banach Spaces ◽  
Local Stability ◽  
Interpolation Method ◽  
Complex Interpolation ◽  
Analytic Family ◽  
Köthe Spaces ◽  
The Stability ◽  
Stability Results ◽  
Differential Process

We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit circle while there is no (bounded) stability for families of four or more Köthe spaces. In the context of arbitrary pairs of Banach spaces, we present some local stability results and some global isometric stability results.

A variation formula for the topological entropy of convex-cocompact manifolds

2010 ◽  
Vol 31 (6) ◽  
pp. 1849-1864 ◽  
Author(s):  
SAMUEL TAPIE
Keyword(s):  
Hausdorff Dimension ◽  
Explicit Formula ◽  
Topological Entropy ◽  
Geodesic Flow ◽  
Kleinian Group ◽  
Limit Set ◽  
Analytic Family ◽  
Variation Formula ◽  
Sectional Curvatures ◽  
Convex Cocompact

AbstractLet (M,gλ) be a 𝒞2-family of complete convex-cocompact metrics with pinched negative sectional curvatures on a fixed manifold. We show that the topological entropy htop(gλ) of the geodesic flow is a 𝒞1 function of λ and we give an explicit formula for its derivative. We apply this to show that if ρλ(Γ)⊂PSL2(ℂ) is an analytic family of convex-cocompact faithful representations of a Kleinian group Γ, then the Hausdorff dimension of the limit set Λρλ(Γ) is a 𝒞1 function of λ. Finally, we give a variation formula for Λρλ (Γ).

scholarly journals An analytic family of representations for the mapping class group of punctured surfaces

2014 ◽  
Vol 18 (3) ◽  
pp. 1485-1538
Author(s):  
Francesco Costantino ◽  
Bruno Martelli
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class ◽  
Analytic Family

Meromorphic multifunctions in complex dynamics

1992 ◽  
Vol 12 (1) ◽  
pp. 39-52 ◽  
Author(s):  
L. Baribeau ◽  
T. J. Ransford
Keyword(s):  
Critical Points ◽  
Complex Dynamics ◽  
Julia Set ◽  
Kleinian Groups ◽  
Rational Maps ◽  
Analytic Family ◽  
Limit Sets ◽  
Upper Semicontinuous ◽  
Open Set ◽  
Similar Vein

AbstractLet {RA} be an analytic family of rational maps and denote by j(λ) the Julia set of Rλ. We prove that the upper semicontinuous regularization j(λ) of j(λ) (which coincides with j(λ) for all λ in a dense open set) is a meromorphic multifunction, and give applications that illustrate the instability of Julia sets. In a similar vein, we also consider forward orbits of critical points and limit sets of Kleinian groups.

ON THE MULTIPLICITIES OF FAMILIES OF COMPLEX HYPERSURFACE-GERMS WITH CONSTANT MILNOR NUMBER

2013 ◽  
Vol 24 (03) ◽  
pp. 1350021 ◽  
Author(s):  
CAMILLE PLENAT ◽  
DAVID TROTMAN
Keyword(s):  
Tangent Cone ◽  
Milnor Number ◽  
Analytic Family ◽  
Singular Set ◽  
Analytic Hypersurface ◽  
Hypersurface Singularities

We show that the possible drop in multiplicity in an analytic family F(z, t) of complex analytic hypersurface singularities with constant Milnor number is controlled by the powers of t. We prove equimultiplicity of μ-constant families of the form f + tg + t2h if the singular set of the tangent cone of {f = 0} is not contained in the tangent cone of {h = 0}.

scholarly journals Interpolation of an analytic family of operators on variable exponent Morrey spaces

2018 ◽  
Vol 48 (3) ◽  
pp. 335-346
Author(s):  
Alexander Meskhi ◽  
Humberto Rafeiro ◽  
Muhammad Asad Zaighum
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Analytic Family

Blow Analytic Mappings and Functions

1993 ◽  
Vol 36 (4) ◽  
pp. 497-506
Author(s):  
Etsuo Yoshinaga
Keyword(s):  
Analytic Functions ◽  
Classical Theorem ◽  
Analytic Family ◽  
Isolated Singularities ◽  
Inverse Mapping ◽  
Continuous Map ◽  
Inverse Mapping Theorem ◽  
Blowing Up ◽  
Analytic Mappings

AbstractLet π: M —> Rn be the blowing-up of Rn at the origin. Then a continuous map-germ f: (Rn — 0,0) —> Rm is called blow analytic if there exists an analytic map-germ such that Then an inverse mapping theorem for blow analytic mappings as a generalization of classical theorem is shown. And the following is shown. Theorem: The analytic family of blow analytic functions with isolated singularities admits an analytic trivialization after blowing-up.

Analytic and coanalytic families of almost disjoint functions

2008 ◽  
Vol 73 (4) ◽  
pp. 1158-1172 ◽  
Author(s):  
Bart Kastermans ◽  
Juris Steprāns ◽  
Yi Zhang
Keyword(s):  
Analytic Family ◽  
Maximality Condition ◽  
Almost Disjoint

AbstractIf is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable , no member of which is covered by finitely many functions from , there is such that for all there are infinitely many integers k such that f(k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality condition.

scholarly journals Analytic family of post-merger template waveforms

2017 ◽  
Vol 95 (12) ◽  
Author(s):  
Walter Del Pozzo ◽  
Alessandro Nagar
Keyword(s):  
Analytic Family
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