The near-horizon geometries of the extremal Kerr black hole and certain generalizations thereof are considered. Their isometry groups are all given by SL(2,R) × U(1). The usual boundary conditions of the Kerr/CFT correspondence enhance the U(1) isometry to a Virasoro algebra. Various alternatives to these boundary conditions are explored. Partial classifications are provided of the boundary con...

at each point z 2 H, making it a model of the hyperbolic plane. Consider the closed compact surface = H= . We aim to show that its isometry group is …nite, and furthermore that we can achieve a sharp upper bound directly proportional to the genus of the surface. Consider, by comparison, the isometries of R=Z, the Euclidean torus T . Any Euclidean translation of R descends to an isometry of T , ...

New G 2 holonomy metrics, D6 branes with inherent U (1) × U (1) isometry and γ-deformations Abstract It is found the most general local form of the 11-dimensional supergravity backgrounds which, by reduction along one isometry, give rise to IIA supergravity solutions with a RR field and a non trivial dilaton, and for which the condition F (1,1) = 0 holds. This condition is stronger than the usu...

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

We consider four-dimensional spacetimes (M,g) which obey the Einstein equations G = T, and admit a global spacelike G1 = R isometry group. By means of dimensional reduction and local analyis on the reduced (2 + 1) spacetime, we obtain a sufficient condition on T which guarantees that (M,g) cannot contain apparent horizons. Given any (3 + 1) spacetime with spacelike translational isometry, the n...

The restricted isometry condition. The proof that the Restricted Isometry Condition is sufficient for sparse recovery using convex programming is due to Candes and Tao [2]. A simpler proof, also due to Candes and Tao, is in [4]. Applications of restricted isometries to vector quantization and democratic coding are found in [10], and applications to computing the condition number of random matri...

This paper improves bounds for restricted isometry constant (RIC) in compressed sensing. Let Φ be a m × n real matrix and k be a positive integer with k ≤ n. The main results of this paper show that if the restricted isometry constant of Φ satisfies δk+ak < 3 2 − 1 + √ (4a+ 3)2 − 8 8a for a > 3 8 , then k-sparse solution can be recovered exactly via l1 minimization in the noiseless case. In par...

A map T: Ej —► E2 (E|, E2 Banach spaces) is an e-isometry if III T(X) T(Y)\\ \\X Y\\ I < e whenever X, Ye Ex. The problem of uniformly approximating such maps by isometries was first raised by Hyers and Ulam in 1945 and subsequently studied for special infinite dimensional Banach spaces. This question is here broached for the class of finite dimensional Banach spaces. The only positive homogene...