In this work, we obtain an analog of Donoho-Stark theorem for the second Hankel-Clifford transform for functions in \(f \in L^1_{\mu} \cap L^2_{\mu}\), using the properties of this transform.

In this paper, we consider the Schwarz boundary value problem for higher-order complex partial differential equations on a triangle. We first introduce the poly-Schwarz operator and the T-type operator for the triangle, and then investigate the boundary behavior of these operators. In addition, we discuss the solvability conditions and present an explicit solution to the Schwarz problem for the inhomoheneous polyanalytic equation on the triangle.

The aim of this paper is to give a characterization of Hardy-Fofana spaces via Riesz transforms. This characterization allows us to describe the distributions belonging to these spaces as a bounded solutions of Cauchy-Riemann’s general temperature equations.

The optical soliton solution of nonlinear complex models holds significant importance in nonlinear optics and communication systems. Considering nonlinear complex models, often described by equations like the nonlinear Schrodinger equation (NLSE), plays a crucial role in defining the balance between dispersive and nonlinear effects, enabling the formation and maintenance of solitons over long distances. This stability is crucial for signal integrity in optical communication systems. The investigation of optical soliton solutions from nonlinear complex models is sometimes complicated. With this in mind, we employed an effective method of extended Tanh function with a Riccatti differential equation to retrieve the dark, singular and periodic wave solutions for the weakly nonlocal nonlinear Schrodinger equation with parabolic law. The obtained solutions were verified by back-substitution in the original equations, with the aid of a Mathematica to affirm the robustness of the chosen approach. Respective 2D and 3D graphs for some of the obtained results was portrayed by choosing suitable values of the parameters that were involved. An analysis of instability that results in the modulation of the steady-state as a result of co-action between the nonlinear and dispersive effects was performed on the proposed model where the condition for stable wave under small perturbation was obtained and presented. The gain spectrum plot for the modulation instability was portrayed.

Using the q-Jackson integral and some elements of the q-harmonic analysis associated with the q-Bessel operator for fixed 0 < q < 1, we introduce the q-Bessel multiplier operators and we give some new results related to these operators as Plancherel’s, Calderón’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. Next, using the theory of reproducing kernels we give best estimates and an integral representation of the extremal functions related to these operators on weighted Sobolev spaces.

In this paper, first we focus on the slicing of negative plurisubharmonic currents which are finite sums involving currents arising from analytic subsets with geometric complete intersection. Next, we provide significant results on the integrability across analytic subsets, of the coefficients of such currents and of their slices.

In this paper, we investigate the stability of specially orthogonally functional equations deriving from additive and quadratic functions4f(x+y)+4f(x−y)+10f(x)+14f(−x)−3f(y)−3f(−y)=f(2x+y)+f(2x−y)andf(x+y+z/2)+f(x+y−z/2)+f(x−y+z/2)+f(y+z−x/2)=f(x)+f(y)+f(z)where f is a mapping from Abelian group to a non-Archimedean space. By adopting a new method, we have made an attempt to prove the Hyers-Ulam stability in non-Archimedean spaces.

The concept of frame is an exciting, dynamic, and fast-paced subject with applications in numerous fields of mathematics and engineering. The purpose of this paper is to introduce equivalent ∗-continuous frames and to present ordinary duals of constructed ∗-continuous frames by an adjointable and invertible operator. Also, we establish some properties.

For the parameter appearing non-linearly in the drift coefficient of homogeneous Itô stochastic differential equation having a stationary ergodic solution, the paper obtains the strong consistency of an approximate maximum likelihood estimator based on Stratonovich type approximation of the continuous Girsanov likelihood, under some regularity conditions, when the corresponding diffusion is observed at equally spaced dense time points over a long time interval in the high frequency regime. Pathwise convergence of stochastic integral approximations and their connection to discrete drift estimators is studied. Often it is shown that discrete drift estimators converge in probability. We obtain convergence of the estimator with probability one. Ornstein-Uhlenbeck process is considered as an example.

In this manuscript, we investigate the unilateral problem for a viscoelastic beam equation of p-Laplacian type. The competition of the strong damping versus the logarithmic source term is considered. We use the potential well theory. Taking into account the initial data is in the stability set created by the Nehari surface, we prove the existence and uniqueness of global solutions by using the penalization method and Faedo-Galerkin’s approximation.