The properties of solutions of the equation u′′(t) = p1(t)u(τ1(t)) + p2(t)u′(τ2(t)) are investigated where pi : [a, +∞[→ R (i = 1, 2) are locally summable functions, τ1 : [a, +∞[→ R is a measurable function and τ2 : [a, +∞[→ R is a nondecreasing locally absolutely continuous one. Moreover, τi(t) ≥ t (i = 1, 2), p1(t) ≥ 0, p2(t) ≤ (4− ε)τ ′ 2(t)p1(t), ε = const > 0 and ∫ +∞ a (τ1(t)− t)p1(t)dt <...

We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. As a physical application one can think of a resistorinductor-varactor circuit with a periodic (or quasi-periodic) forcing function, even if the range of applicability of the theory is much wider. In the limit of large...

We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasiperiodic analytic forcing term and in the presence of damping. As a physical application one can think of a resistor– inductor–varactor circuit with a periodic sor quasiperiodicd forcing function, even if the range of applicability of the theory is much wider. In the limit of large...

In this paper we generalize the classical theorems of Brown and Halmos about algebraic properties Toeplitz operators to Bergman spaces over unit ball in several complex variables. A key result, which is independent interest, characterization summable functions u on whose Berezin transform can be written as a finite sum ∑jfjg¯j with all fj,gj being holomorphic. particular, show that such functio...

In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracial state on this algebra which proves the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of f...