Related papers: Invariant Modules and the Reduction of Nonlinear P…
The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…
For every positive integral level $k$ we study arithmetic properties of certain holomorphic modular forms associated to modular invariant spaces spanned by graded dimensions of $L_{\hat{sl_2}}(k \Lambda_0)$-modules. We found a necessary and…
Existence and global regularity results for boundary-value problems of Robin type for harmonic and polyharmonic functions in $n$-dimensional half-spaces are offered. The Robin condition on the normal derivative on the boundary of the…
Finite-dimensional spaces which are invariant under the action of the Hamiltonian of the BC_N Inozemtsev model are introduced, and it is shown that higher commuting operators also preserve the finite-dimensional spaces. The relationship…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first…
For a linear ODE with indeterminate coefficients, we explicitly exhibit a fundamental system of solutions, in terms of the coefficients. We show that the generalized Wronskians of the fundamental system are given by an action of the Schur…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
In this paper invariant subspace method has been employed for solving linear and non-linear fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the…
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…
We find modular transformations of normalized characters for the following $W$-algebras: (a) $W^{min}_k(\frak{g})$, where $\frak{g}=D_n \, (n \geq 4)$, or $E_6$, $E_7$, $E_8$, and $k$ is a negative integer $\geq -2$, or $\geq…
A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
The paper concerns the investigation of nonconvex and nondifferentiable integral functionals on general Banach spaces, which may not be reflexive and/or separable. Considering two major subdifferentials of variational analysis, we derive…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…