منابع مشابه
Multidimensional Baker-Akhiezer Functions and Huygens’ Principle
A notion of rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in C is introduced. It is proved that BA function exists only for very special configurations (locus configurations), which satisfy certain overdetermined algebraic system. The BA functions satisfy some algebraically integrable Schrödinger equations, so any locus configuration determines such an equation...
متن کاملHelicoids with handles and Baker-Akhiezer spinors
For more then 200 years the helicoid was the only known infinite total curvature embedded minimal surface of finite topology. The situation changed in 1993, when Hoffman, Karcher and Wei [9] discovered the genus one helicoid a minimal torus with one end, which has a form of the helicoid at infinity. The genus one helicoid was constructed using the Weierstrass representation. Karcher, Wei and Ho...
متن کاملCombinatorial aspects of the Baker-Akhiezer functions for S2
We show here that a certain sequence of polynomials arising in the study of S2 m-quasi invariants satisfies a 3-term recursion. This leads to the discovery that these polynomials are closely related to the Bessel polynomials studied by Luc Favreau. This connection reveals a variety of combinatorial properties of the sequence of Baker–Akhiezer functions for S2. In particular we obtain in this ma...
متن کاملA Riemann-Hilbert approach to the Akhiezer polynomials.
In this paper, we study those polynomials, orthogonal with respect to a particular weight, over the union of disjoint intervals, first introduced by N. I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This approach complements the method proposed in a previous paper, which involves the construction of a certain meromorphic function on a hyperelliptic Rieman...
متن کاملOrthogonality Relations and Cherednik Identities for Multivariable Baker–akhiezer Functions
We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summati...
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ژورنال
عنوان ژورنال: Physics Today
سال: 2000
ISSN: 0031-9228,1945-0699
DOI: 10.1063/1.1325211