×

zbMATH — the first resource for mathematics

On the scaling limit of a singular integral operator. (English) Zbl 1138.45008
Summary: The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems.
MSC:
45P05 Integral operators
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
39A05 General theory of difference equations
44A15 Special integral transforms (Legendre, Hilbert, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Birkhoff G.D. (1913). The generalized Riemann problem for linear differential equations and allied problems for linear difference and q-difference equations. Proc. Amer. Acad. Arts Sci. 49: 521–568 · JFM 44.0391.03
[2] Borodin A. (2004). Isomonodromy transformations of linear systems of difference equations. Ann. Math. 160: 1141–1182 · Zbl 1085.39001
[3] Harnad J. and Its A.R. (2002). Integrable Fredholm operators and dual isomonodromic deformations. Commun. Math. Phys. 226: 497–530 · Zbl 1008.34082
[4] Krichever I.M. (2004). Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem. Russian Math. Surveys 59: 1117–1154 · Zbl 1075.39012
[5] Ladyzhenskaya, O., Uraltseva, N.: Linear and Quasilinear Elliptic Equations. Academic Press (1968) · Zbl 0164.13002
[6] Stein E.M. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press (1993) · Zbl 0821.42001
[7] Tracy C.A. and Widom H. (1994). Fredholm determinants, differential equations and matrix models. Commun. Math. Phys. 163: 33–72 · Zbl 0813.35110
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.