Discreetness of Spectrum of Schrödinger Operator on
Riemannian Manifold by using Lebesgue Measure

Farah Diyab; B. Surender Reddy

doi:https://doi.org/10.14445/22315373/IJMTT-V68I8P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 8 | Year 2022 | Article Id. IJMTT-V68I8P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I8P507

Discreetness of Spectrum of Schrödinger Operator on Riemannian Manifold by using Lebesgue Measure

Farah Diyab, B. Surender Reddy

Received	Revised	Accepted	Published
30 Jun 2022	01 Aug 2022	13 Aug 2022	24 Aug 2022

Abstract

We formulate the conditions for discreteness Dirichlet spectrum of Schrödinger operator 𝐻 = −𝛥 + 𝑉(𝑥) on Riemannian Manifold. Its formulated by using Lebesgue measure instead of harmonic capacity. We also provide the recent related results.

Keywords

Dirichlet problem, Spectrum, Manifolds, Schrödinger, Spectral Geometry.

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Citation :

Farah Diyab, B. Surender Reddy, "Discreetness of Spectrum of Schrödinger Operator on Riemannian Manifold by using Lebesgue Measure," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 8, pp. 67-71, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I8P507