Non-symmetric fast decreasing polynomials and applications
نویسندگان
چکیده
منابع مشابه
Fast decreasing and orthogonal polynomials
This paper reviews some aspects of fast decreasing polynomials and some of their recent use in the theory of orthogonal polynomials. 1. Fast decreasing polynomials Fast decreasing, or pin polynomials have been used in various situations. They imitate the ”Dirac delta” best among polynomials of a given degree. They are an indispensable tool to localize results and to create well localized ”parti...
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The determination of the support of the equilibrium measure in the presence of an external field is important in the theory of weighted polynomials on the real line. Here we present a general condition guaranteeing that the support consists of at most two intervals. Applying this to the external fields associated with fast decreasing polynomials, we extend previous results of Totik and Kuijlaar...
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The symmetric Macdonald polynomials are able to be constructed out of the non-symmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their non-symmetric counterparts. In taking this approach we are able to obtain new results as well as simpler and more accessible derivations of some of the known fundamental ...
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Generalizing the classical Capelli identity has recently attracted a lot of interest ([HU], [Ok], [Ol], [Sa], [WUN]). In several of these papers it was realized, in various degrees of generality, that Capelli identities are connected with certain symmetric polynomials which are characterized by their vanishing at certain points. From this point of view, these polynomials have been constructed b...
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In (1.2) mκ(z) is the monomial symmetric function in the variables z1, . . . , zN , and the sum is over all partitions μ which have the same modulus as κ but are smaller in dominance ordering. The polynomials Pκ possess a host of special properties, and in fact form the natural basis for a class of symmetric multivariable orthogonal polynomials generalizing the classical orthogonal polynomials ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.03.006