Related papers: Certain composition formulae for the fractional in…
In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions. The basis functions in each angular momentum subspace are of the form…
For $\alpha \in \mathbb{R}$, let $\mathscr{D}_\alpha$ denote the scale of Hilbert spaces consisting of Dirichlet series $f(s) = \sum_{n=1}^\infty a_n n^{-s}$ that satisfy $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$. The…
In this paper, we study the complex symmetry of weighted composition-differentiation operator $D_{n, \psi, \phi}$ on weighted Bergman spaces $\mathcal{A}^2_{\alpha}$ with respect to the conjugation $C_{\mu, \eta}$ for $\mu, \eta \in \{z\in…
Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians $H$ with complex energy eigenvalues are considered. The method of evaluation of quantities $\sigma_n$ known as the singular values of $H$ is proposed. Its basic…
We realize norms of most composition operators acting on the Hardy space with linear fractional symbol as roots of hypergeometric functions. This realization leads to simple necessary and sufficient conditions on the symbol to exhibit…
This paper presents some new propositions related to the fractional order $h$-difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order $h$-difference…
We characterize the class of weights related to the boundedness of variable fractional maximal operator $M_{\beta(\cdot),r(\cdot)}$ on variable Lebesgue spaces. This extend previously known results, including those corresponding to the…
In this paper, we characterize bounded, compact and order bounded sum of weighted differentiation composition operators from Bergman type spaces to weighted Banach spaces of analytic functions, where the sum of weighted differentiation…
Using the $H^\infty$-functional calculus for quaternionic operators, we show how to generate the fractional powers of some densely defined differential quaternionic operators of order $m\geq 1$, acting on the right linear quaternionic…
In the present paper we derive a unified new integral whose integrand contains products of Fox $H$-function and a general class of polynomials having general arguments. A large number of integrals involving various simpler functions follow…
We find a lower bound for the essential norm of the difference of two composition operators acting on $H^2(B_N)$ or $A^2_s(B_N)$ ($s>-1$). This result plays an important role in proving a necessary and sufficient condition for the…
In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels $$K(x,y)=\frac{\Omega_1(x-A_1 y)}{|x-A_1 y |^{\frac{n}{q_1}}} \cdots \frac{\Omega_m(x-A_m y)}{|x-A_m y…
Integral transforms $$(\mbox{\boldmath$H$}f)(x)=\int^\infty_0H^{m,n}_{\thinspace p,q} \left[xt\left|\begin{array}{c}(a_i,\alpha_i)_{1,p}\\[1mm](b_j,\beta_j)_{1,q} \end{array}\right.\right]f(t)dt$$ involving Fox's $H$-functions as kernels…
Under simple hypotheses on the nonlinearity $f$, we consider the fractional harmonic operator problem \begin{equation}\label{abstr}\sqrt{-\Delta+|x|^2}\,u=f(x,u)\ \ \textrm{in }\ \mathbb{R}^N\end{equation} or, since we work in the extension…
In this paper, we study a family of fractional integral operators whose kernel carrying a critical index has singularity on the light-cone in R^n+1.
This paper considers various integrals where the integrand includes the log gamma function (or its derivative, the digamma function) multiplied by a trigonometric or hyperbolic function. Some apparently new integrals and series are…
A complex scalar k is said to be an extended eigenvalue of a bounded linear operator A on a complex Hilbert space if there is a nonzero operator X such that AX=kXA. There are some solutions to the problem of computing the extended…
In this paper, the following iterated commutators $T_{*,\Pi b}$ of maximal operator for multilinear singular integral operators and $I_{\alpha, \Pi b}$ of multilinear fractional integral operator are introduced and studied $$\aligned…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
We identify the semigroups consisting of bounded composition operators on the Hardy spaces $H^p(\U)$ of the upper half-plane. We show that any such semigroup is strongly continuous on $H^p(\U)$ but not uniformly continuous and we identify…