The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the harmonic confining force, the hyperbolic and the trigonometric, we demonstrate the following for all the root systems: (i) Construction of a complete set of quantum conserved quantities in terms of a total...

In the present investigation, inspired by work on Yamaguchi type class of analytic functions satisfyingthe criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in openunit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use S\v{a}l\v{a}gean-difference operator, which is a special Dunkl operator with constant $\vartheta$ $\Delta$ , wedesignate definite new classes $\mathcal{R}_{\lam...

Abstract We study the Li–Yau inequality for heat equation corresponding to Dunkl harmonic oscillator, which is a nonlocal Schrödinger operator parameterized by reflections and multiplicity functions. In particular case when reflection group isomorphic ℤ 2 d {\mathbb{Z}...

algebraic frames are generalizations of fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. the paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discret...

suppose $t$ and $s$ are moore-penrose invertible operators betweenhilbert c*-module. some necessary and sufficient conditions are given for thereverse order law $(ts)^{ dag} =s^{ dag} t^{ dag}$ to hold.in particular, we show that the equality holds if and only if $ran(t^{*}ts) subseteq ran(s)$ and $ran(ss^{*}t^{*}) subseteq ran(t^{*}),$ which was studied first by greville [{it siam rev. 8 (1966...