TY - JOUR
T1 - Essential Self-Adjointness and the L2 -Liouville Property
AU - Hua, Bobo
AU - Masamune, Jun
AU - Wojciechowski, Radosław K.
N1 - Funding Information:
B.H. is supported by NSFC, Grants Numbers 11831004 and 11926313. J.M. is supported in part by JSPS KAKENHI Grant Numbers 18K03290 and 17H01092. R.W. is supported by PSC-CUNY Awards, jointly funded by the Professional Staff Congress and the City University of New York, and the Collaboration Grant for Mathematicians, funded by the Simons Foundation.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/4
Y1 - 2021/4
N2 - We discuss connections between the essential self-adjointness of a symmetric operator and the constancy of functions which are in the kernel of the adjoint of the operator. We then illustrate this relationship in the case of Laplacians on both manifolds and graphs. Furthermore, we discuss the Green’s function and when it gives a non-constant harmonic function which is square integrable.
AB - We discuss connections between the essential self-adjointness of a symmetric operator and the constancy of functions which are in the kernel of the adjoint of the operator. We then illustrate this relationship in the case of Laplacians on both manifolds and graphs. Furthermore, we discuss the Green’s function and when it gives a non-constant harmonic function which is square integrable.
UR - http://www.scopus.com/inward/record.url?scp=85102693308&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85102693308&partnerID=8YFLogxK
U2 - 10.1007/s00041-021-09833-2
DO - 10.1007/s00041-021-09833-2
M3 - Article
AN - SCOPUS:85102693308
SN - 1069-5869
VL - 27
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 2
M1 - 26
ER -