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Generic injectivity and stabilityissues are discussed and some Fredholm alternatives are considered for connections in[MP20MP20, Zho17Zho17].

Instead, we show belowthat aω satisfies a G̊arding’s inequality. Then, according to Fredholm’s alternative,uniqueness implies existence of solution. ... Because of Lemma 3.2 we knowthat the problem satisfies Fredholm’s alternative (see for

dµ(w). In order to manipulate the regularized Fredholm determinant we approximate the right handside by.

18. J.M. Lee, Fredholm operators and Einstein metrics on conformally compact manifolds,Memoirs AMS, in press, math.DG/0105046.

ρ̄h(ū) =2. πc. 1. 1dv̄ K(ū, v̄) ρ̄h(v̄). (2.46). It is of Fredholm-type and may be immediately expanded in the small parameter c anditeratively solved as

dress an important and challenging set of problems: computation of Fredholm and Volterra. ... been already noted in the computation of spectra of Fredholm operators. •

is. given by. π(HY ,T) = ind(T),. where ind(T) is the Fredholm index of T.

In particular, we identify the Fredholm deter-minant of the integral equation inverting the nonlocal ̄-dressing problem with the τ -function. ... Then, by the Fredholm alternative, the homogeneousequation with η = 0 has only the trivial solution.

Dispersive hydrodynamics of soliton condensates forthe Korteweg-de Vries equation. T. Congy, G.A. El, G. Roberti, and A. Tovbis. Abstract. We consider large-scale dynamics of non-equilibrium dense soliton gas for theKorteweg-de Vries (KdV) equation

One reason explaining the spectral gap as above is the fact that LM is an (un-bounded) Fredholm operator in the v variable, of the form.