Real clifford windowed Fourier transform

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.     

Wavelets associated with Hankel transform and their Weyl transforms

The Hankel transform is an important transform. In this paper, we study thewavelets associated with the Hankel transform, then define the Weyl transform of thewavelets. We give criteria of its boundedness and compactness on the L~p-spaces.     

关于广义Aluthge变换的数值域

设T是作用在希尔伯特空间H上的有界线性算子,本文研究T的广义Aluthge变换和广义＊-Aluthge变换,并且得到T的广义Aluthge变换的数值域和广义＊-Aluthge变换的数值域相等．     

A new construction of the Clifford-Fourier kernel

In this paper, we develop a new method based on the Laplace transform to study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier transform in the Laplace domain is obtained. When the dimension is even, the inverse Laplace transform may be computed and we obtain the explicit expression for the kernel as a finite sum of Bessel functions. We equally obtain the plane wave decomposition and find new integral representations for the kernel in all dimensions. Finally we define and compute the formal generating function for the even dimensional kernels.     

Statistical properties of the Hough transform estimator in the presence of measurement errors

The Hough transform is a common computer vision algorithm used to detect shapes in a noisy image. Originally the Hough transform was proposed as a technique for detection of straight lines in images. In this paper we study the statistical properties of the Hough transform estimator in the presence of measurement errors. We consider the simple case of detection of one line parameterized in polar coordinates. We show that the estimator is consistent, and possesses a rate of convergence of the cube-root type. We derive its limiting distribution, and study its robustness properties. Numerical results are discussed as well. In particular, based on extensive experiments, we define a “rule of thumb” for the determination of the optimal width parameter of the template used in the algorithm.     

Some remarks on the Brylinski-Radon and the Fourier transforms

We will study a relationship between the Brylinski-Radon and the Fourier transforms of a monodromic perverse sheaf. In fact we will show that they are equivalent modulo a constant perverse sheaf. As an application, we will discuss a relation between the Sklyanin transform and the Brylinski-Radon transform.     

A Pettis-type integral and applications to transition semigroups

Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.     

Generalized spherical Aluthge transforms and binormality for commuting pairs of operators

In this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set inclusion diagrams among normal, quasinormal, centered, and Campbell binormal commuting pairs of operators.     

Generalized principal pivot transforms, complementarity theory and their applications in stochastic games

In this article, we revisit the concept of principal pivot transform and its generalization in the context of vertical linear complementarity problem. We study solution set and solution rays of a vertical linear complementarity problem. Finally we present an application of generalized principal pivot transform in game theory.     

Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms

We define and study the Fourier-Wigner transform associated with the Dunkl operators,and we prove for this transform an inversion formula.Next,we introduce and study the Weyl transforms W_σ associated with the Dunkl operators,where cr is a symbol in the Schwartz space S(R~d×R~d).An integral relation between the precedent Weyl and Wigner transforms is given.At last,we give criteria in terms of σ for boundedness and compactness of the transform W_σ.     

Deformations of Real Rational Dynamics in Tropical Geometry

In this paper we study analytic properties of orbits given by real rational functions. We introduce some comparison methods which allow us to compare the real rational dynamics with automata given by (max, +) functions, passing through a kind of scale transform in tropical geometry. Such a scale transform gives a one-to-one correspondence of presentations between automata and real rational functions. We study invariant properties of the real rational dynamics under change of presentations of automata.     

Segal-Bargmann transform and Paley-Wiener theorems on <Emphasis Type="Italic">M</Emphasis>(2)

We study the Segal-Bargmann transform on M(2). The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer’s type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of M(2). We also prove a Paley-Wiener theorem for the inverse Fourier transform.     

Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups

In this article, we present the abstract harmonic analysis aspects of the operator-valued continuous Gabor transform (CGT) on second countable, non-unimodular, and type I locally compact groups. We show that the operator-valued continuous Gabor transform CGT satisfies a Plancherel formula and an inversion formula. As an example, we study these results on the continuous affine group.     

The Airy equation with nonlocal conditions

We study a third-order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed, we use a nonlocal condition, which specifies a weighted integral of the solution over the spatial interval. Via adaptations of the Fokas transform method (or unified transform method), we obtain a solution representation for this problem. We also study the time periodic analog of this problem, and thereby obtain long time asymptotics for the original problem with time periodic boundary and nonlocal data.     

Legendre Transform and Applications to Finite and Infinite Optimization

We investigate convex constrained nonlinear optimization problems and optimal control with convex state constraints in the light of the so-called Legendre transform. We use this change of coordinate to propose a gradient-like algorithm for mathematical programs, which can be seen as a search method along geodesics. We also use the Legendre transform to study the value function of a state constrained Mayer problem and we show that it can be characterized as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.     

Linearized inverse scattering based on seismic reverse time migration

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse time migration (RTM). In the process, the explicit evaluation of the so-called normal operator is avoided, while other differential and pseudodifferential operator factors are introduced. We prove that, under certain conditions, the transform yields a partial inverse, and support this with numerical simulations. In addition, we explain the recently discussed ‘low-frequency artifacts’ in RTM, which are naturally removed by the new method.     

A two-dimensional ruin problem on the positive quadrant

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that either of the insurance companies is ruined in finite time. Subsequently, for exponentially distributed claims, we derive an explicit analytical expression for this joint ruin probability by explicitly inverting this Laplace transform. We also provide a characterization of the Laplace transform of the joint ruin time.     

On paranormed Zweier ideal convergent sequence spaces defined By Orlicz function

In this article we introduce paranorm ideal convergent sequence spaces using Zweier transform and Orlicz function. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces.     

Busy period analysis of the state dependent M/M/1/K queue

In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform.     

Inversion Formula for Shearlet Transform in Arbitrary Space Dimensions

In this article, we study the convergence of the inverse shearlet transform in arbitrary space dimensions. For every pair of admissible shearlets, we show that although the integral involved in the inversion formula from the continuous shearlet transform is convergent in the L² sense, it is not true in general whenever pointwise convergence is considered. We give some su?cient conditions for the pointwise convergence to hold. Moreover, for any pair of admissible shearlets we show that the Riemannian sums defined by the inverse shearlet transform are convergent to the original function as the sampling density tends to infinity.