Related papers: Exact Evaluation Of Some Highly Oscillatory Integr…
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results…
Oscillations are a powerful tool for building examples of colorings witnessing negative partition relations. We survey several results illustrating the general technique and present a number of applications.
We obtain $L^2$ decay estimates in $\lambda$ for oscillatory integral operators whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of…
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$…
In this letter we apply a method recently devised in \cite{aapla03} to find precise approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in \cite{aapla03} is refined and results of much…
We prove that integral points can be effectively determined on all but finitely many modular curves, and on all but one modular curve of prime power level.
The definition of infinite dimensional Fresnel integrals is generalized to the case of polynomial phase functions of any degree and applied to the construction of a functional integral representation of the solution of a general class of…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a general signature assumption on the phase. This simultaneously generalises earlier work of the…
The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality…
We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that…
It is proved that nonlinear integral equations of certain class have global solution and estimates of the solution are given as $t\to \infty$.
In this article we provide a motivation for studying integrals $\displaystyle \int_0^{\frac{\pi}{2}}x\cos^mx~dx$, $m\in \mathbb{N}$. We demonstrate several properties of this class of integrals and show that it is closely related to the…
In this note we discuss the complex version of the Higgs oscillator on the hyperbolic space. The eigenvalues and resonances of the complex Higgs oscillator are computed in different examples in the hyperbolic setting. We also propose open…
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta. These derivations are then…
We show how the integral formula of Poisson for holomorphic functions on the right half plane can be used to quickly evaluate certain integrals from the Table of Gradshteyn and Ryzhik. In addition, we prove a version of this formula for…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
The full description of the stable factor-representations of the infinite hyperoctahedral group up to quasi-equivalence obtained.