NDLI: How to Find a Measure from its Potential

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

Computational Methods and Function Theory : Volume 17

Computational Methods and Function Theory : Volume 16

Computational Methods and Function Theory : Volume 15

Computational Methods and Function Theory : Volume 14

Computational Methods and Function Theory : Volume 13

Computational Methods and Function Theory : Volume 12

Computational Methods and Function Theory : Volume 11

Computational Methods and Function Theory : Volume 10

Computational Methods and Function Theory : Volume 9

Computational Methods and Function Theory : Volume 8

Computational Methods and Function Theory : Volume 8, Issue 2, May 2008

Majorization of the Modulus of Continuity of Analytic Functions

Uniqueness of Entire Functions and Their Derivatives

Schwarz-Pick Inequalities for the Schur-Agler Class on the Polydisk and Unit Ball

Some Relatives of the Hardy-Stein-Spencer Identities

On the Lower Order of Locally Univalent Functions

Asymptotics for Polynomial Zeros: Beware of Predictions from Plots

Dieudonné Points of Holomorphic Self-Maps of Regions

Uniqueness of Harmonic Mappings into Strictly Starlike Domains

Spectral Notions for Conformal Maps: a Survey

On the Growth of the Dirichlet Integral for Some Function Spaces

Derivatives of Meromorphic Functions with Multiple Zeros and Rational Functions

Derivation-Invariant Subspaces of C∞

High Energy Eigenfunctions of One-Dimensional Schrödinger Operators with Polynomial Potentials

Some Trigonometric and Elliptic Integrals

Fourier-Bessel Series for Second-Order and Fourth-Order Bessel Differential Equations

Extreme and Support Points of the Class of Non-Vanishing Univalent Functions

Analytic Number Theory and Statistics

How to Find a Measure from its Potential

A Note on the Hayman-Wu Theorem

The Structure of Certain Spaces of Analytic Functions

Computational Methods and Function Theory : Volume 8, Issue 1, May 2008

Computational Methods and Function Theory : Volume 7

Computational Methods and Function Theory : Volume 6

Computational Methods and Function Theory : Volume 5

Computational Methods and Function Theory : Volume 4

Computational Methods and Function Theory : Volume 3

Computational Methods and Function Theory : Volume 2

Computational Methods and Function Theory : Volume 1

How to Find a Measure from its Potential

Content Provider	Springer Nature Link
Author	Pritsker, Igor
Copyright Year	2008
Abstract	We consider the problem of finding a measure from the given values of its logarithmic potential on the support. It is well known that a solution to this problem is given by the generalized Laplacian. The case of our main interest is when the support is contained in a rectifiable curve, and the measure is absolutely continuous with respect to the arclength on this curve. Then the generalized Laplacian is expressed by a sum of normal derivatives of the potential. Such a representation is already available for smooth curves, and we show it holds for any rectifiable curve in the plane. We also relax the assumptions imposed on the potential.Finding a measure from its potential often leads to another closely related problem of solving a singular integral equation with Cauchy kernel. The theory of such equations is well developed for smooth curves. We generalize this theory to the class of Ahlfors regular curves and arcs, and characterize the bounded solutions on arcs.
Starting Page	597
Ending Page	614
Page Count	18
File Format	PDF
ISSN	16179447
Journal	Computational Methods and Function Theory
Volume Number	8
Issue Number	2
e-ISSN	21953724
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-01-24
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	integral equations Computational Mathematics and Numerical Analysis measure Functions of a Complex Variable boundary values Integration, integrals of Cauchy type, integral representations of analytic functions Analysis Integral representations, integral operators, integral equations methods Cauchy singular integral Boundary value and inverse problems Potential
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Analysis

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

Cauchy integral and singular integral operator over closed Jordan curves

A Method for Computing Nearly Singular Integrals

A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions

The Riemann–Hilbert Problem in Weighted Classes of Cauchy Type Integrals with Density from L $^{ P( · )}$(Γ)

Application of Cauchy integrals and singular integral equations in scattered data problems

On the application of GMRES to oscillatory singular integral equations

Minkowski Dimension and Cauchy Transform in Clifford Analysis

The Continuation Approach: A General Framework for the Analysis and Evaluation of Singular and Near-Singular Integrals

The Carleman Type Singular Integral Equations

How to Find a Measure from its Potential

Similar Documents

Cauchy integral and singular integral operator over closed Jordan curves

A Method for Computing Nearly Singular Integrals

A Grid-Based Boundary Integral Method for Elliptic Problems in Three Dimensions

The Riemann–Hilbert Problem in Weighted Classes of Cauchy Type Integrals with Density from L $^{ P( · )}$(Γ)

Application of Cauchy integrals and singular integral equations in scattered data problems

On the application of GMRES to oscillatory singular integral equations

Minkowski Dimension and Cauchy Transform in Clifford Analysis

The Continuation Approach: A General Framework for the Analysis and Evaluation of Singular and Near-Singular Integrals

The Carleman Type Singular Integral Equations

How to Find a Measure from its Potential