6 papers
Weighted discrete tori and weighted trigonometric sums
Shuofeng Huang, Chengjie Yu
In this paper, we obtain a weighted trigonometric summation formula which is an extension of the trigonometric summation formula by Grigor'yan, Lin and Yau \cite{GLY}.
An extension of Katsuda-Urakawa's Faber-Krahn inequality
Wankai He, Chengjie Yu
In this paper, motivated by our previous work \cite{HY}, we prove that the minimum of the first Dirichlet eigenvalues for the normalized combinatorial -Laplacian on connected fi…
Faber-Krahn inequalities for first Dirichlet eigenvalues of combinatorial -Laplacian on graphs with boundary
Wankai He, Chengjie Yu
In this paper, we obtain sharp Faber-Krahn inequalities for the first Dirichlet eigenvalue of the combinatorial -Laplacian on connected graphs with a fixed number of vertices or…
Sharp Gagliardo-Nirenberg inequality and logarithmic Sobolev inequality on integer lattices
Yongjie Shi, Chengjie Yu
In this paper, we obtain a sharp Garliardo-Nirenberg inequality on integer lattices and characterize its rigidity. Moreover, as a consequence of the sharp Garliardo-Nirenberg inequ…
Extension and rigidity of Perrin's lower bound estimate for Steklov eigenvalues on graphs
Yongjie Shi, Chengjie Yu
In this paper, we extend a lower bound estimate for Steklov eigenvalues by Perrin \cite{Pe} on unit-weighted graphs to general weighted graphs and characterise its rigidity.
Comparisons of Dirichlet, Neumann and Laplacian eigenvalues on graphs and their applications
Yongjie Shi, Chengjie Yu
In this paper, we obtain some comparisons of the Dirichlet, Neumann and Laplacian eigenvalues on graphs. We also discuss their rigidities and some of their applications including s…