A product estimate, the parabolic Weyl lemma and applications

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Application of Hopf's lemma on contact CR-warped product submanifolds of a nearly Kenmotsu manifold

In this paper we consider contact CR-warped product submanifolds of the type $M = N_Ttimes_f N_perp$, of a nearly Kenmotsu generalized Sasakian space form $bar M(f_1‎, ‎f_2‎, ‎f_3)$ and by use of Hopf's Lemma we show that $M$ is simply contact CR-product under certain condition‎. ‎Finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case is dis...

Pseudodifferential Multi-product Representation of the Solution Operator of a Parabolic Equation

By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on Rn as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof i...

An observability estimate for parabolic equations from a measurable set in time and its applications

Abstract. This paper presents a new observability estimate for parabolic equations in × (0, T ), where  is a convex domain. The observation region is restricted over a product set of an open nonempty subset of  and a subset of positive measure in (0, T ). This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property f...

An observability estimate for parabolic equations from a mesurable set in time and its applications

Abstract. This paper presents a new observability estimate for parabolic equations in × (0, T ), where  is a convex domain. The observation region is restricted over a product set of an open nonempty subset of  and a subset of positive measure in (0, T ). This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property f...