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On the long tail property of product convolution
Let X and Y be two independent random variables with corresponding distributions F and G on [0 ,∞ ). The distribution of the product XY , which is...
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Swarm Simulation Modeling Using the Hadamard Product
AbstractUsing a large number of drones poses the challenge of correct, transparent, and high-performance modeling of their co-operation as a swarm....
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Convolution Quadrature for Hyperbolic Symbols
In this chapter we introduce the operational calculus that forms the basis of the analysis of the problems this book investigates, i.e., we give a...
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Arithmetic Convolution
A function \(f:\mathbb {N}\setminus \{0\}\rightarrow \mathbb {C}\)...
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Convolution Method and Non-Positive Functions
In our installment of the convolution method, the estimates in Lemma 8.1 and 10.2...
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On certain GL(6) form and its Rankin-Selberg convolution
We consider L G ( s ) to be the L -function attached to a particular automorphic form G on GL (6). We establish an upper bound for the mean square estimate...
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Bounds on shifted convolution sums for Hecke eigenforms
Shifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke...
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Product of Pseudo-Differential Operators Associated with Zero Order Mehler-Fock Transform
In this paper, the dual convolution structure for the Mehler-Fock transform is defined and obtained its estimates on Lebesgue space. Next, the two...
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Closure Properties for Heavy-Tailed and Related Distributions An Overview
This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail...
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A new convolution operator for the linear canonical transform with applications
The linear canonical transform plays an important role in engineering and many applied fields, as it is the case of optics and signal processing. In...
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Large Perturbations of a Magnetic System with Stein–Weiss Convolution Nonlinearity
In this work we consider a non-local magnetic system with a Stein–Weiss convolution potential. Using variational methods, we study the existence of...
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Method of Maximal Monotonic Operators in the Theory of Nonlinear Integro-Differential Equations of Convolution Type
Using the method of maximal monotonic (in the Browder–Minty sense) operators, we prove global theorems on the existence and uniqueness of solutions...
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Covariant CP-Instruments and Their Convolution Semigroups
Using probability operators and Fourier transforms of CP-instruments on von Neumann algebras, we give necessary and sufficient conditions for...
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Product Measures
In this chapter, we define product measures, and prove the famous Fubini theorem. As a typical application, we compute the volume of the unit ball in...
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An overview on a time discrete convolution—space collocation BEM for 2D exterior wave propagation problems
We consider 2D transient linear wave propagation problems defined in the exterior of bounded domains. In particular, we first consider the problem...
