Geometrical aspects of spectral theory and value distribution for Herglotz functions
type: Item
instance of: scholarly article
title: Geometrical aspects of spectral theory and value distribution for Herglotz functions
zbMATH Open document ID: 1027.47038
DOI: 10.1023/A:1022410108020
author: S. V. Breimesser
author: D. B. Pearson
published in: Mathematical Physics, Analysis and Geometry
publication date: 2003-05-11T00:00:00Z
review text: The authors show how the spectral theory for Herglotz functions and differential operators is related to and dependent on the geometrical properties of the complex upper half-plane, viewed as a hyperbolical space. They next establish the theory of value distribution for real-valued Lebesgue measurable functions \(f\) and introduce the value distribution function associated with any given Herglotz function \(F\). The theory of value distribution for boundary values of Herglotz functions is related to the description of asymptotics for solutions of the Schrödinger equation on the half-line.
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 1908554
zbMATH Keywords: Herglotz functions
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: \(m\)-function
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: spectral theory
zbMATH Keywords: value distribution
reviewed by: Svatoslav Staněk
MaRDI profile type: Publication
Recommended article: Generalized value distribution for Herglotz functions and spectral theory
Recommended article: Geometric aspects of multiparameter spectral theory
Recommended article: Q3477529
Recommended article: Spectral theory of Herglotz functions and their compositions
Recommended article: Spectrum Estimates and Applications to Geometry
Recommended article: Q4324353
Recommended article: Holomorphic spectral theory: a geometric approach
Recommended article: Spectral properties of classical integral operators and geometry
Recommended article: The spectrum of the Laplacian: A geometric approach
Recommended article: On summability of distributions and spectral geometry
description: scientific article; zbMATH DE number 1908554