Let \(\mathcal{D}'(\mathbb{R}^n)\) and \(\mathcal{E}'(\mathbb{R}^n)\) be the spaces of distributions compactly supported on \(\mathbb{R}^n\), \(n\geq 2\) respectively, let \(\mathcal{E}'_{\natural}(\mathbb{R}^n)\) space all radial (invariant under rotations \(mathbb{R}^n\)) in \(\mathcal{E}'(\mathbb{R}^n)\), let\(\widetilde{T}\) spherical transform (Fourier–Bessel transform) a distribution \(T\...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

The kinetic energy of a multi-particle system is described by the one-particle density matrix τ(x,y). Alongside γ(x,y) it one key objects in quantum-mechanical approximation schemes. We prove asymptotic formula λk∼(Bk)−2, B⩾0, as k→∞, for eigenvalues λk self-adjoint operator T⩾0 with kernel