He Jun SUN

6286

Universal inequalities and bounds for weighted eigenvalues of the Schrödinger operator on the Heisenberg group

For a bounded domain W in the Heisenberg group Hn, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator - DHn +V, where DHn is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for DHn in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian D and the Schrödinger operator -D+V on a domain in Rn and other manifolds.
Anahtar Kelimeler:

Eigenvalue, universal inequality, Heisenberg group, Schrödinger operator, Kohn Laplacian

Universal inequalities and bounds for weighted eigenvalues of the Schrödinger operator on the Heisenberg group

For a bounded domain W in the Heisenberg group Hn, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator - DHn +V, where DHn is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for DHn in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian D and the Schrödinger operator -D+V on a domain in Rn and other manifolds.
Keywords:

Eigenvalue, universal inequality, Heisenberg group, Schrödinger operator, Kohn Laplacian,

PDF
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
Sayıdaki Diğer Makaleler

On graded prime and primary submodules

Ünsal TEKİR, Ahmet Göksel AĞARGÜN, Kürşat Hakan ORAL

Universal inequalities and bounds for weighted eigenvalues of the Schrödinger operator on the Heisenberg group

He Jun SUN

Invariant subspace problem for positive L-weakly and M-weakly compact operators

Erdal BAYRAM, Cevriye TONYALI

Properties of RD-projective and RD-injective modules

Lixin MAO

Nilpotent elements and reduced rings

Libin LI, Junchao WEI

Existence theory for positive solutions of p-laplacian multi-point BVPs on time scales

You Hui SU

Krull dimension of types in a class of first-order theories

Domenico ZAMBELLA

Homology with respect to a kernel transformation

Seyed Naser HOSSEINI, Mohammad Zaher Kazemi BANEH

Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces

Ajay K. SHARMA

A note on weighted Ap(G)-modules

Serap ÖZTOP