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The proof of the following theorem known till now is based on the martingale theory (see e.g. We give a \pure dyadic analysis" proof for it.. Theorem 5. [AVD]), then can be
Although Theorem 1.3 gives solutions to the same equation as Theorem 1.1 (if m is the same), the spirit is quite different: While m could take any value in Theorem 1.1 , we have here
The following theorem proves Schur’s congruence for scaled Legendre polynomials. The proof is identical to Wahab’s for the usual
The Cauchy type singular integral equation is investigated when the line of integration is the union of a countable number of disconnected segments.. The equation is
For instance, the delay equation does not inherit the classical properties of the Dirichlet boundary value prob- lem for the heat equation: the maximum principle is not valid,
Bifurcation of transversal homoclinics is studied for a pair of ordinary differential equations with periodic perturbations when the first unperturbed equa- tion has a manifold
In order to apply the upper and lower solutions method to fractional differential equation two-point boundary value problem (1.. 1) complete the proof of the theorem.. We consider
The Radon Nikodym Theorem plays a key role in our proof of the Fundamen- tal Theorem of Calculus, particularly the proof given by Bradley [4], so we will outline this proof but
