Linearly recursive sequences and operator polynomials
نویسندگان
چکیده
منابع مشابه
From Sequences to Polynomials and Back, via Operator Orderings
Non-commutativity is a common feature in mathematical modeling of reality which, in quantum mechanics, introduces the so-called Heisenberg-Weyl algebra. This new quality does not come without a price − the order of components in operator successions is now relevant and has to be carefully traced in calculations. A traditional solution to this problem is to standardize the notation by fixing the...
متن کاملMaximal and Linearly Inextensible Polynomials
Let S(n, 0) be the set of monic complex polynomials of degree n ≥ 2 having all their zeros in the closed unit disk and vanishing at 0. For p ∈ S(n, 0) denote by |p|0 the distance from the origin to the zero set of p. We determine all 0-maximal polynomials of degree n, that is, all polynomials p ∈ S(n, 0) such that |p|0 ≥ |q|0 for any q ∈ S(n, 0). Using a second order variational method we then ...
متن کاملDiophantine equations for second order recursive sequences of polynomials
Let B be a nonzero integer. Let define the sequence of polynomials Gn(x) by G0(x) = 0, G1(x) = 1, Gn+1(x) = xGn(x) +BGn−1(x), n ∈ N. We prove that the diophantine equation Gm(x) = Gn(y) for m,n ≥ 3, m 6= n has only finitely many solutions.
متن کاملLinearly Unrelated Sequences
There are not many new results concerning the linear independence of numbers. Exceptions in the last decade are, e.g., the result of Sorokin [8] which proves the linear independence of logarithmus of special rational numbers, or that of Bezivin [2] which proves linear independence of roots of special functional equations. The algebraic independence of numbers can be considered as a generalizati...
متن کاملOn linearly related sequences of difference derivatives of discrete orthogonal polynomials
Let ν be either ω ∈ C \ {0} or q ∈ C \ {0, 1}, and let Dν be the corresponding difference operator defined in the usual way either by Dωp(x) = p(x+ω)−p(x) ω or Dqp(x) = p(qx)−p(x) (q−1)x . Let U and V be two moment regular linear functionals and let {Pn(x)}n≥0 and {Qn(x)}n≥0 be their corresponding orthogonal polynomial sequences (OPS). We discuss an inverse problem in the theory of discrete ort...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90496-b