Appell polynomials and their relatives II. Boolean theory
نویسندگان
چکیده
منابع مشابه
Appell Polynomials and Their Relatives Ii. Boolean Theory
The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the other two being free and tensor/classical probability). The basic properties of the Boolean Appell polynomials are described. In particular, their generatin...
متن کاملAppell Polynomials and Their Relatives
This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...
متن کاملAppell Polynomials and Their Relatives Iii. Conditionally Free Theory
ABSTRACT. This paper describes the analogs of the Appell polynomial families in the context of algebras with two states, also called the c-free probability theory, introduced by Bożejko, Speicher, and Leinert. This theory includes as two extreme cases the free and Boolean probability theories. We prove recursions, generating functions, and factorization and martingale properties for these polyn...
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∞ n=0 pn(x)t n or, equivalently, p′n(x) = pn−1(x). If g(t) is an entire function, g(0) 6= 0, with at least one zero, the asymptotics of linearly scaled polynomials {pn(nx)} are described by means of finitely zeros of g, including those of minimal modulus. As a consequence, we determine the limiting behavior of their zeros as well as their density. The techniques and results extend our earlier w...
متن کاملOn Multiple Appell Polynomials
In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2009
ISSN: 0022-2518
DOI: 10.1512/iumj.2009.58.3523