EXPANSION IN GENERALIZED EIGENFUNCTIONS FOR LAPLACIANS ON GRAPHS AND METRIC MEASURE SPACES

作     者：Lenz, Daniel Teplyaev, Alexander 

作者机构：Univ Jena Math Inst D-07743 Jena Germany Univ Connecticut Dept Math Storrs CT 06269 USA 

出 版 物：《TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY》 (美国数学会汇刊)

年 卷 期：2016年第368卷第7期

页      面：4933-4956页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：German Research Foundation (DFG) NSF [DMS-0505622] Direct For Mathematical & Physical Scien Division Of Mathematical Sciences Funding Source: National Science Foundation 

主　　题：EIGENFUNCTIONS BOUNDARY value problems -- Numerical solutions DIFFERENTIAL equations -- Numerical solutions HILBERT space LAPLACIAN matrices 

摘      要：We consider an arbitrary selfadjoint operator in a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions, in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces consisting of general eigenfunctions. This automatically gives a Plancherel type formula. For suitable operators on metric measure spaces we discuss some growth restrictions on the generalized eigenfunctions. For Laplacians on locally finite graphs the generalized eigenfunctions are exactly the solutions of the corresponding difference equation.