We set up precision holography for the non-conformal branes preserving 16 supersymmetries. The near-horizon limit of all such p-brane solutions with p ≤ 4, including the case of fundamental string solutions, is conformal to AdSp+2 × S8−p with a linear dilaton. We develop holographic renormalization for all these cases. In particular, we obtain the most general asymptotic solutions with appropri...

The theory of Hilbert spaces of entire functions [1] was developed by Louis de Branges in the late 1950s and early 1960s with the help of his students including James Rovnyak and David Trutt. It is a generalization of the part of Fourier analysis involving Fourier transform and Plancherel formula. The de Branges-Rovnyak theory of square summable power series, which played an important role in l...

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We give two applications of this result, one of them to a problem arising from probability theory.

In this survey we present a brief history and the basic ideas of the generalized fractional calculus (GFC). The notion “generalized operator of fractional integration” appeared in the papers of the jubilarian Prof. S.L. Kalla in the years 1969-1979 when he suggested the general form of these operators and studied examples of them whose kernels were special functions as the Gauss and generalized...

The sum of all the ladder and rainbow diagrams in φ3 theory near 6 dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in terms of generalized hypergeometric functions; the expansion and representation of these functions ca...

Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor. We prove a “Fun...

We define a new class of positive and Lebesgue measurable functions in termsof their asymptotic behavior, which includes the class of regularly varying functions.We also characterize it by transformations, corresponding to generalized momentswhen these functions are random variables. We study the properties of this new classand discuss their applications to Extreme Value The...

Making use of Linear operator theory, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belonging to this new class. The results are generalized to families with fixed finitely ma...