An application to Kato's square root problem

Kato’s Square Root Problem in Banach Spaces

Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

Square-root quantization: application to quantum black holes

In this short paper we present two different quantizations of the simple one-dimensional model selfgravitating spherically symmetric thin shell. Fortunately enough, both ways of quantization lead to exactly solvable problems and we obtained mass spectra of the shell, analyzed them and extracted the quantum black hole spectra. The first approach can be called a proper time quantization. By using...

Square - Root Algorithmsfor the Discrete Logarithm Problem ( a Survey )

Square Root Problem of Kato for the Sum of Operators

This paper is concerned with the square root problem of Kato for the ”sum” of linear operators in a Hilbert space H. Under suitable assumptions, we show that if A and B are respectively m-scetroial linear operators satisfying the square root problem of Kato. Then the same conclusion still holds for their ”sum”. As application, we consider perturbed Schrödinger operators.

Square-root rule of two-dimensional bandwidth problem

The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for...