Related papers: Perturbed Bessel operators

In this paper, we investigate the $W^{s,p}$-boundedness for stationary wave operators of the Schr\"odinger operator with inverse-square potential $$\mathcal L_a=-\Delta+\tfrac{a}{|x|^2}, \quad a\geq -\tfrac{(d-2)^2}{4},$$ in dimension…

In this paper we analyze the convergence of the following type of series \begin{equation*} T_N f(x)=\sum_{j=N_1}^{N_2} v_j\Big(\mathcal{P}_{a_{j+1}} f(x)-\mathcal{P}_{a_{j}} f(x)\Big),\quad x\in \mathbb R_+, \end{equation*} where…

The differential expression $L_m=-\partial_x^2 +(m^2-1/4)x^{-2}$ defines a self-adjoint operator H_m on L^2(0;\infty) in a natural way when $m^2 \geq 1$. We study the dependence of H_m on the parameter m, show that it has a unique…

We prove that for a homogeneous linear partial differential operator $\mathcal A$ of order $k \le 2$ and an integrable map $f$ taking values in the essential range of that operator, there exists a function $u$ of special bounded variation…

We determine the asymptotic behaviour of the $n$th derivatives of the Bessel functions $J_\nu(a)$ and $K_\nu(a)$, where $a$ is a fixed positive quantity, as $n\to\infty$. These results are applied to the asymptotic evaluation of two…

In this paper, we consider the characterizations of the Lipschitz spaces and homogeneous Lipschitz spaces associated to the biharmonic operator $\Delta^2.$ With this characterizations, we prove the boundedness of the Bessel potentials,…

In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries…

We study the Hp-Lq boundedness of certain integral operators of fractional type.

Let $\Delta$ be the Laplace--Beltrami operator acting on a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$ with $m > n \ge 3$. Let $\frak{h}_t(x,y)$ be the kernels of the semigroup $e^{-t\Delta}$ generated by $\Delta$.…

Weakly centered and spectrally weakly cenetered weighted composition operators in $L^2$-spaces are characterized. Criteria for existence of invariant subspaces are given. Additional results and examples are supplied.

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f), $$ which appears in the theory of Bessel functions. The…

In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…

We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.

Consider a non-doubling manifold with ends $M = \mathfrak{R}^{n}\sharp\, {\mathbb R}^{m}$ where $\mathfrak{R}^n=\mathbb{R}^n\times \mathbb{S}^{m-n}$ for $m> n \ge 3$. We say that an operator $L$ has a generalised Poisson kernel if $\sqrt{…

We have used recent integral representations of the derivatives of the Bessel functions with respect to the order to obtain closed-form expressions in terms of generalized hypergeometric functions and Meijer-$G$ functions. Also, we have…

We investigate the traceability of positive integral operators on $L^2(X,\mu)$ when $X$ is a Hausdorff locally compact second countable space and $\mu$ is a non-degenerate, $\sigma$-finite and locally finite Borel measure. This setting…

We prove some existence results for a class of nonlinear fractional equations driven by a nonlocal operator.

The spectral analysis of the Sturm-Liouville operator defined on a finite segment is the subject of an extensive literature. Sturm-Liouville operators on a finite segment are well studied and have numerous applications. The study of such…

Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…

We establish boundedness estimates for solutions of generalized porous medium equations of the form $$ \partial_t u+(-\mathfrak{L})[u^m]=0\quad\quad\text{in $\mathbb{R}^N\times(0,T)$}, $$ where $m\geq1$ and $-\mathfrak{L}$ is a linear,…