منابع مشابه
Wronskians and Linear Independence
Obviously, a family of linearly dependent functions has a zero Wronskian. Many standard textbooks on differential equations (e.g., [10, Chap. 5, §5.2], [22, Chap. 1, §4], [9, Chap. 3, §7]) contain the following warning: linearly independent functions may have an identically zero Wronskian! This seems to have been pointed out for the first time by Peano [20, 21], who gave the example of the pair...
متن کاملIntegrals of products of eigenfunctions on SL 2 ( C )
In a variety of situations, integrals of products of eigenfunctions have faster decay than smoothness entails. This phenomenon does not appear for abelian or compact groups, since irreducibles are finite-dimensional, so the decomposition of a tensor product of irreducibles is finite. In contrast, for non-compact, nonabelian groups irreducibles are typically infinite-dimensional, and the decompo...
متن کاملGeneralized Wronskians and Weierstrass Weights
Given a point P on a smooth projective curve C of genus g, one can determine the Weierstrass weight of that point by looking at a certain Wronskian. In practice, this computation is difficult to do for large genus. We introduce a natural generalization of the Wronskian matrix, which depends on a sequence of integers s = m0, . . . ,mg−1 and show that the determinant of our matrix is nonzero at P...
متن کاملWronskians, Cyclic Group Actions, and Ribbon Tableaux
The Wronski map is a finite, PGL2(C)-equivariant morphism from the Grassmannian Gr(d, n) to a projective space (the projectivization of a vector space of polynomials). We consider the following problem. If Cr ⊂ PGL2(C) is a cyclic subgroup of order r, how may Cr-fixed points are in the fibre of the Wronski map over a Cr-fixed point in the base? In this paper, we compute a general answer in term...
متن کاملWronskians, Generalized Wronskians and Solutions to the Korteweg-de Vries Equation
A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate positons, negatons and their interaction solutions to the Korteweg-de Vries equation. Moreover, general positons and negatons are constructed through the Wro...
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ژورنال
عنوان ژورنال: Ufa Mathematical Journal
سال: 2020
ISSN: 2074-1863,2074-1871
DOI: 10.13108/2020-12-2-3