We provide a treatment of algebro-geometric solutions of the classical massive Thirring system in the framework of the Weierstrass–Klein theory of hyperelliptic functions. We show that the equations of this model generate the characteristic relations of hyperelliptic theory of even hyperelliptic curves, the same role that the KdV equation plays for odd hyperelliptic curves. We also consider the...

The g-function was introduced by Affleck and Ludwig in the context of critical quantum systems with boundaries. In the framework of the thermodynamic Bethe ansatz (TBA) method for relativistic scattering theories, all attempts to write an exact integral equation for the off-critical version of this quantity have, up to now, been unsuccesful. We tackle this problem by using an n-particle cluster...

Given a density d de…ned on the Borel subsets of [0;1); the limit at in…nity in density of a function f : [0;1) ! R is zero if each of the sets ft : jf(t)j "g has zero density whenever " > 0: It is proved that every Lebesgue integrable function f : [0;1) ! R veri…es this type of behavior at in…nity with respect to a scale of densities including the usual one, d(A) = limr!1 m(A\[0;r)) r : The an...

We denote by x a real variable and by n a positive integer variable. The reference measure on the real line R is the Lebesgue measure. In this note we will use only basic properties of the Lebesgue measure and integral on R. It is well known that the fact that a function tends to zero at infinity is a condition neither necessary nor sufficient for this function to be integrable. However, we hav...

In this paper we obtain the discrete integrable self-dual network hierarchy associated with a spectral problem. On basis of theory algebraic curves, continuous flow and related to are straightened using Abel-Jacobi coordinates. The meromorphic function Baker-Akhiezer introduced on hyperelliptic curve. Quasi-periodic solutions constructed help asymptotic properties algebra-geometric characters f...

If f is a Henstock-Kurzweil integrable function on the real line, the Alexiewicz norm of f is ‖f‖ = sup I | ∫ I f | where the supremum is taken over all intervals I ⊂ . Define the translation τx by τxf(y) = f(y − x). Then ‖τxf − f‖ tends to 0 as x tends to 0, i.e., f is continuous in the Alexiewicz norm. For particular functions, ‖τxf − f‖ can tend to 0 arbitrarily slowly. In general, ‖τxf − f‖...