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Formulas for Surface Weighted Numbers on Graph

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Formulas for Surface Weighted Numbers on Graph

Ghulam Hazrat Aimal Rasa

Ghulam Hazrat Aimal Rasa "Formulas for Surface Weighted Numbers on Graph" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-3, April 2022, pp.784-790, URL: https://www.ijtsrd.com/papers/ijtsrd49573.pdf

The boundary value problem differential operator on the graph of a specific structure is discussed in this article. The graph has degree 1 vertices and edges that are linked at one common vertex. The differential operator expression with real-valued potentials, the Dirichlet boundary conditions, and the conventional matching requirements define the boundary value issue. There are a finite number of eig?nv?lu?s in this problem.The residues of the diagonal elements of the Weyl matrix in the eigenvalues are referred to as weight numbers. The ?ig?nv?lu?s are monomorphic functions with simple poles.The weight numbers under consideration generalize the weight numbers of differential operators on a finite interval, which are equal to the reciprocals of the squared norms of eigenfunctions. These numbers, along with the eig?nv?lu?s, serve as spectral data for unique operator reconstruction. The contour integration is used to obtain formulas for surfacethe weight numbers, as well as formulas for the sums in the case of superficial near ?ig?nv?lu?s. On the graphs, the formulas can be utilized to analyze inverse spectral problems.

boundaryproblem, Formulas for Surface, weight numbers

Volume-6 | Issue-3, April 2022
IJTSRD | www.ijtsrd.com | E-ISSN 2456-6470
Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0)

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