2,290 research outputs found
Orthogonal Expansion of Real Polynomials, Location of Zeros, and an L2 Inequality
AbstractLet f(z)=a0φ0(z)+a1φ1(z)+…+anφn(z) be a polynomial of degree n, given as an orthogonal expansion with real coefficients. We study the location of the zeros of f relative to an interval and in terms of some of the coefficients. Our main theorem generalizes or refines results due to Turán and Specht. In particular, it includes a best possible criterion for the occurrence of real zeros. Our approach also allows us to establish a weighted L2 inequality giving a lower estimate for the product of two polynomials
Multiparameter Riesz Commutators
It is shown that product BMO of Chang and Fefferman, defined on the product
of Euclidean spaces can be characterized by the multiparameter commutators of
Riesz transforms. This extends a classical one-parameter result of Coifman,
Rochberg, and Weiss, and at the same time extends the work of Lacey and
Ferguson and Lacey and Terwilleger on multiparameter commutators with Hilbert
transforms. The method of proof requires the real-variable methods throughout,
which is new in the multi-parameter context.Comment: 38 Pages. References updated. To appear in American J Mat
Exceptional Laguerre polynomials
The aim of this paper is to present the construction of exceptional Laguerre
polynomials in a systematic way, and to provide new asymptotic results on the
location of the zeros. To describe the exceptional Laguerre polynomials we
associate them with two partitions. We find that the use of partitions is an
elegant way to express these polynomials and we restate some of their known
properties in terms of partitions. We discuss the asymptotic behavior of the
regular zeros and the exceptional zeros of exceptional Laguerre polynomials as
the degree tends to infinity.Comment: To appear in Studies in Applied Mathematic
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related
to continued fraction expansions is summarized and an attempt is made to
describe the influence of Stieltjes' ideas and work in research done after his
death, with an emphasis on the theory of orthogonal polynomials
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