MAT 280: Laplacian Eigenfunctions: Theory, Applications, and Computations Lectures 14: Shape Recognition Using Laplacian Eigenvalues and Computational Methods of Laplacian Eigenvalues/Eigenfunctions

MAT 280: Laplacian Eigenfunctions: Theory, Applications, and Computations Lectures 12+13: Laplacian Eigenvalue Problems for General Domains: IV. Asymptotics of the Eigenvalues

MAT 280: Laplacian Eigenfunctions: Theory, Applications, and Computations Lecture 20: Introduction to Spectral Graph Theory–III. Graph Cut and Cheeger Constants, Isospectral Graphs, and Discrete Laplacian Eigenvalue Problems

Example 1.2. In Figure 1, S is the set of dark nodes, and the dotted lines form ∂S. S ∆ = V \S. Also, vol(S) = m(S) ∆ = x∈S m(x).

Seidel Signless Laplacian Energy of Graphs

Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...

Inverse nodal problem for p-Laplacian with two potential functions

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...