Related papers: Estimates for generalizated oscillatory integrals …
In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional…
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite…
We generalize the Stein-Tomas [17] $L^2$-restricition theorem and the uniform Sobolev estimates of Kenig, Ruiz and the second author [11] by allowing critically singular potential. We also obtain Strichartz estimates for Schr\"odinger and…
In this paper we develop a theory for oscillatory integrals with complex phases. When $f:{\mathbb C}^n \to {\mathbb C}$, we evaluate this phase function on the basic character ${\rm e}(z) := e^{2\pi i x} e^{2\pi i y}$ of ${\mathbb C} \simeq…
The aim of this paper is to study generalized q-analogs of the well-known q-deformed harmonic oscillators and to connect them with q-Hermite polynomials. We give a construction of the appropriate oscillator-like algebras and show that…
In paper this paper it is considered the summation problem for trigonometric integrals with quadratic phase. This problem considered in the papers \cite{Chub},\cite{Chax},\cite{Jabbar} in particular cases. Our results generalized the…
We prove a bilinear $L^2(\R^d) \times L^2(\R^d) \to L^2(\R^{d+1})$ estimate for a pair of oscillatory integral operators with different asymptotic parameters and phase functions satisfying a transversality condition. This is then used to…
We prove a global uniform Artin-Rees lemma type theorem for sections of ample line bundles over smooth projective varieties. This result is used to prove an Artin-Rees lemma for the polynomial ring with uniform degree bounds. The proof is…
Starting from the nonlinear ODE $z'' + f(t)\,z + g(t)\, z^{m}=0$ with $m>1$, we show that after a suitable normal-form reduction of any Hill equation one may, without loss of generality, fix the linear part as $f(t)\equiv \omega^{2}$ (with…
In the present paper we establish sharp pointwise estimates on the polyharmonic Green function and its derivatives in an arbitrary bounded open set.
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…
We consider fractional relaxation and fractional oscillation equations involving Erdelyi-Kober integrals. In terms of Riemann-Liouville integrals, the equations we analyze can be understood as equations with time-varying coefficients.…
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.
This paper is concerned with uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and $L^\infty$ estimates for the pressure as…
We give an exact result about the asymptotic limit of an oscillatory integral whose phase contains a certain flat term. Corresponding to the real analytic phase case, one can see an essential difference in the behavior of the above…
We present a study dealing with a novel phase reconstruction method based on iterated Hilbert transform embeddings. We show results for the Stuart-Landau oscillator observed by generic observables. The benefits for reconstruction of the…
In the present paper, we were mainly concerned with obtaining estimates for the general Taylor-Maclaurin coefficients for functions in a certain general subclass of analytic bi-univalent functions. For this purpose, we used the Faber…
We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of smooth estimators parameterized by \alpha dominating the James-Stein estimator. The estimator for \alpha=1 corresponds to…
This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated…