Spectral properties of harmonic Toeplitz operators and applications to the perturbed Krein Laplacian

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dc.contributor.authorBruneau, Vincent
dc.contributor.authorRaikov, Georgi
dc.date.accessioned2025-01-23T21:22:04Z
dc.date.available2025-01-23T21:22:04Z
dc.date.issued2018
dc.description.abstractWe consider harmonic Toeplitz operators T-V = PV :H(Omega) -> H(Omega) where P : L-2(Omega) -> H(Omega) is the orthogonal projection onto H(Omega) = {u is an element of L-2 (Omega)) vertical bar Delta u = 0 in Omega}, Omega subset of R-d, d >= 2, is a bounded domain with boundary partial derivative Omega is an element of C-infinity and V : Omega -> C is an appropriate multiplier. First, we complement the known criteria which guarantee that T-V is in the pth Schatten-von Neumann class S-p, by simple sufficient conditions which imply T-V is an element of S-p(,w), the weak counterpart of S-p. Next, we consider symbols V >= 0 which have a regular power-like decay of rate & nbsp;gamma > 0 at partial derivative Omega, and we show that T-V is unitarily equivalent to a classical pseudo-differential operator of order-gamma, self-adjoint in L-2 (partial derivative Omega). Utilizing this unitary equivalence, we obtain the main asymptotic term of the eigenvalue counting function for T-V, and establish a sharp remainder estimate. Further, we assume that Omega is the unit ball in R-d, and V = (V) over bar is compactly supported in Omega, and investigate the eigenvalue asymptotics of the Toeplitz operator T-V. Finally, we introduce the Krein Laplacian K, self-adjoint in L-2 (Omega), perturb it by a multiplier V is an element of C((Omega) over bar; R), and show that sigma(ess)(K + V) = V (partial derivative Omega). Assuming that V >= 0 and V-vertical bar partial derivative Omega = 0, we study the asymptotic distribution of the discrete spectrum of K +/- V near the origin, and find that the effective Hamiltonian which governs this distribution is the Toeplitz operator T-V.
dc.fuente.origenWOS
dc.identifier.doi10.3233/ASY-181467
dc.identifier.eissn1875-8576
dc.identifier.issn0921-7134
dc.identifier.urihttps://doi.org/10.3233/ASY-181467
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/101243
dc.identifier.wosidWOS:000445000100003
dc.issue.numero1-2
dc.language.isoen
dc.pagina.final74
dc.pagina.inicio53
dc.revistaAsymptotic analysis
dc.rightsacceso restringido
dc.subjectHarmonic Toeplitz operators
dc.subjectKrein Laplacian
dc.subjecteigenvalue asymptotics
dc.subjecteffective Hamiltonian
dc.titleSpectral properties of harmonic Toeplitz operators and applications to the perturbed Krein Laplacian
dc.typeartículo
dc.volumen109
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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