Related papers: Non-divergence evolution operators modeled on H\"o…

Let D be a domain in the quaternionic space H. We prove a differential criterion that characterizes Fueter-regular quaternionic functions f:bD -> H of class C^1. We find differential operators T and N, with complex coefficients, such that a…

We investigate the relation between the invariant operators satisfying the quantum Liouville-von Neumann and the Heisenberg operators satisfying the Heisenberg equation. For time-dependent generalized oscillators we find the invariant…

We show a right unitary transformation approach based on Susskind-Glogower operators that diagonalizes a generalized Dicke Hamiltonian in the field basis and delivers a tridiagonal Hamiltonian in the Dicke basis. This tridiagonal…

This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective…

Let O be the minimal nilpotent adjoint orbit in a classical complex semisimple Lie algebra g. O is a smooth quasi-affine variety stable under the Euler dilation action $C^*$ on g. The algebra of differential operators on O is D(O)=D(Cl(O))…

We conjecture that the renormalized perturbative $S$-matrix of quantum field theory coincides with the evolution operator of the standard functional differential Schrodinger equation whose right hand side (quantum local Hamiltonian) is…

We establish unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layer, with explicit lower bounds for the optimal Hardy constant. The approach is based on a quantitative integration-by-parts mechanism…

Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…

The Double Operator Integral (DOI) framework provides a powerful tool for analyzing perturbations and interactions between self-adjoint operators in functional analysis and spectral theory. However, most existing DOI formulations rely on…

We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…

Using a 5D N=1 supersymmetric toy-model compactified on S_1/(Z_2 x Z_2'), with a ``brane-localised'' superpotential, it is shown that higher (dimension) derivative operators are generated as one-loop counterterms to the (mass)^2 of the…

We study the Cauchy problem associated to parabolic systems of the form $D_t\boldsymbol{u}=\boldsymbol{\mathcal A}(t)\boldsymbol u$ in $C_b(\mathbb{R}^d;\mathbb{R}^m)$, the space of continuous and bounded functions…

We exhibit a family of second-order hyperbolic differential operators presenting spectral transition of the Hamilton map. As a consequence we prove that the Cauchy problem is not locally solvable at the origin in Gevrey classes of order…

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in…

We give a detailed description of the resolution of the identity of a second order $q$-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The $q$-difference operator and the two choices of…

We consider second order linear degenerate-elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Guti\'errez and Tournier for the Heisenberg group, we…

In this study, we analyze a semilinear damped evolution equation under different damping conditions, including the undamped $(\theta=0)$, effectively damped $(0<2\theta<\sigma)$, critically damped $(2\theta=\sigma)$, and non-effectively…

This note presents an investigation on the global hypoellipticity problem for Cauchy operators on $\mathbb{T}^{n+1}$ belonging to the class \linebreak $L = \prod_{j=1}^{m}\left(D_t + c_j(t) P_j(D_x)\right)$, where $P_j(D_x)$ is a…

All non-equivalent integrable evolution equations of the fifth order of the form $u_t=D_x\frac{\delta H}{\delta u}$ are found.

Large time behavior of solutions to abstract differential equations is studied. The corresponding evolution problem is: $$\dot{u}=A(t)u+F(t,u)+b(t), \quad t\ge 0; \quad u(0)=u_0. \qquad (*)$$ Here $\dot{u}:=\frac {du}{dt}$, $u=u(t)\in H$,…