The free-space Green function for a two-dimensional exponentially graded elastic medium is derived. The shear modulus μ is assumed to be an exponential function of the Cartesian coordinates (x, y), i.e. μ ≡ μ(x, y) = μ0e12, where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel ...

In the technique known as gridding, the data samples are weighted for sampling density and convolved with a finite kernel, then resampled on a grid preparatory to a fast Fourier transform. The authors compare the artifact introduced into the image for various convolving functions of different sizes, including the Kaiser-Bessel window and the zero-order prolate spheroidal wave function (PSWF). T...

The aim of this paper is to prove new quantitative uncertainty principle for the generalized Fourier transform connected with a Dunkl type operator on the real line. More precisely we prove An Lp-Lq-version of Morgan's theorem.

Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous time random walk on Z and represent the one state occup...

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

In this paper, we consider the normalized Bessel function of index ?>?12, find an integral representation term xnj?+n(x)j?(y). This allows us to establish a product formula for generalized Hankel B??,n on R. is kernel transform F?,n arising from Dunkl theory. Indeed show that B??,n(x)B??,n(y) can be expressed as in terms B??,n(z) with explicit invoking Gegenbauer polynomials all n?N?. The obtai...