46 citations · 207 across the 21 of their papers we have counts for
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Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
Diederik Aerts, Marek Czachor, Maciej Kuna
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier tra…
On the von Neumann equation with time-dependent Hamiltonian. Part II: Applications
Maciej Kuna, Jan Naudts
This second part deals with applications of a general method to describe the quantum time evolution determined by a Schroedinger equation with time-dependent Hamiltonian. A new asp…
Solving the von Neumann equation with time-dependent Hamiltonian. Part I: Method
Maciej Kuna, Jan Naudts
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-de…
Special solutions of nonlinear von Neumann equations
Jan Naudts, Maciej Kuna
We consider solutions of the non-linear von Neumann equation involving Jacobi's elliptic functions sn, cn, and dn, and 3 linearly independent operators. In two cases one can constr…
Covariance systems
Jan Naudts, Maciej Kuna
We introduce new definitions of states and of representations of covariance systems. The GNS-construction is generalized to this context. It associates a representation with each s…