In this note, we study the sub-Laplacian of the 15-dimensional octonionic anti-de Sitter space which is obtained by lifting with respect to the anti-de Sitter fibration the Laplacian of the octonionic hyperbolic space OH<sup>1</sup>. We also obtain two integral representations for the corresponding subelliptic heat kernel.
We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.
Abstract
The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.
Abstract
In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive
single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.
Abstract
We consider analytic and pluriharmonic functions belonging to the classes 𝐵𝑝(Ω) and 𝑏𝑝(Ω) and defined in the ball . The theorems established in the paper make it possible to obtain some integral representations of functions of the above-mentioned classes. The existence of bounded projectors from the space 𝐿(ρ, Ω) into the space 𝐵𝑝(Ω) and from the space 𝐿(ρ, Ω) into the space 𝑏𝑝(Ω) is proved. Also, consideration is given to the existence of boundary values of fractional integrals of functions of the spaces 𝐵𝑝(Ω) and 𝑏𝑝(Ω).
Abstract
Let $\mathcal {W}^{n}$
W
n
be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$
W
∈
W
n
and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$
W
∈
W
are considered.
Invariant operators and integral representations in hyperbolic space.
