This review aims to offer a pedagogical introduction the analytic conformal bootstrap program via journey through selected topics. We methods which include large spin perturbation theory, Mellin space and Lorentzian inversion formula. These techniques are applied variety of topics ranging from large-N theories, epsilon expansion holographic superconformal correlators, demonstrated in number exp...

New type Paley–Wiener theorems for the modified multidimensional Mellin and inverse Mellin transforms are established. The supports of functions are described in terms of their modified Mellin (or inverse Mellin) transform without passing to the complexification.

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the growth of the slope for infinite activity exponential Lévy models. As auxiliary results, we obtain the limiting values of short maturity digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the s...

Let Mδ be the maximum of a standard Bessel bridge of dimension δ. A series formula for P (Mδ ≤ a) due to Gikhman and Kiefer for δ = 1, 2, . . . is shown to be valid for all real δ > 0. Various other characterizations of the distribution of Mδ are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution of Mδ is described both as δ → ∞ and as δ...

We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when t...

We describe a method to compute the inverse Mellin transform of holonomic sequences, that is based on a method to compute the Mellin transform of holonomic functions. Both methods are implemented in the computer algebra package HarmonicSums.

We use the term “stable” to mean numerical stability, that the formal solution of an integral equation can be well-approximated using standard methods, including but not limited to hypergeometric functions or numerical integration. Thus, valid trial solutions may be found by symbolic integration or computerized numerical integration. We specifically analyze a class of forward problems that can ...

An auditory Mellin transform has been proposed to segregate information about the size and shape of the vocal tract automatically; the process is also independent of glottal pitch. In this paper, we describe a method for resynthesizing speech from the Mellin representation using a high quality vocoder (STRAIGHT), and a nonlinear function to map between the two representations of speech. This en...