TY - JOUR
T1 - On the Robin spectrum for the hemisphere
AU - Rudnick, Zeév
AU - Wigman, Igor
N1 - Publisher Copyright:
© 2021, Fondation Carl-Herz and Springer Nature Switzerland AG.
PY - 2022/4
Y1 - 2022/4
N2 - We study the spectrum of the Laplacian on the hemisphere with Robin boundary conditions. It is found that the eigenvalues fall into small clusters close to the Neumann spectrum, and satisfy a Szegő type limit theorem. Sharp upper and lower bounds for the gaps between the Robin and Neumann eigenvalues are derived, showing in particular that these are unbounded. Further, it is shown that except for a systematic double multiplicity, there are no multiplicities in the spectrum as soon as the Robin parameter is positive, unlike the Neumann case which is highly degenerate. Finally, the limiting spacing distribution of the desymmetrized spectrum is proved to be the delta function at the origin.
AB - We study the spectrum of the Laplacian on the hemisphere with Robin boundary conditions. It is found that the eigenvalues fall into small clusters close to the Neumann spectrum, and satisfy a Szegő type limit theorem. Sharp upper and lower bounds for the gaps between the Robin and Neumann eigenvalues are derived, showing in particular that these are unbounded. Further, it is shown that except for a systematic double multiplicity, there are no multiplicities in the spectrum as soon as the Robin parameter is positive, unlike the Neumann case which is highly degenerate. Finally, the limiting spacing distribution of the desymmetrized spectrum is proved to be the delta function at the origin.
KW - Hemisphere
KW - Laplacian
KW - Level spacing distribution
KW - Robin boundary conditions
KW - Robin–Neumann gaps
UR - http://www.scopus.com/inward/record.url?scp=85099772657&partnerID=8YFLogxK
U2 - 10.1007/s40316-021-00155-9
DO - 10.1007/s40316-021-00155-9
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AN - SCOPUS:85099772657
SN - 2195-4755
VL - 46
SP - 121
EP - 137
JO - Annales Mathematiques du Quebec
JF - Annales Mathematiques du Quebec
IS - 1
ER -