NDLI: Shilov boundary and p-adic injective analytic functions

Please wait, while we are loading the content...

Shilov boundary and p-adic injective analytic functions

Content Provider	Springer Nature Link
Author	Escassut, Alain
Copyright Year	2011
Abstract	Let K be an algebraically closed field complete with respect to a dense ultrametric absolute value \|.\|. Let D be an infraconnected affinoid subset of K and let H(D) be the Banach algebra of analytic elements on D. Let f ∈ H(D) be injective in D and let f $_{}$ be the mapping defined on the multiplicative spectrum of H(D) that identifies with the set of circular filters on D. We show that f $_{}$ is injective and maps bijectively the Shilov boundary of H(D) onto this of H(f(D)). Thanks to this property we give a new proof of the equality $\left\| {f(x) - f(y)} \right\| = \left\| {x - y} \right\|\sqrt {\left\| {f'(x)f'(y)} \right\|} $ .
Starting Page	263
Ending Page	280
Page Count	18
File Format	PDF
ISSN	20700466
Journal	P-Adic Numbers, Ultrametric Analysis, and Applications
Volume Number	3
Issue Number	4
e-ISSN	20700474
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-11-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	p-adic meromorphic functions values distribution injective analytic functions Shilov boundary Algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in