On representations of generalized oscillator for two sequences of linearly related orthogonal polynomials

Borzov, V. V.; Damaskinsky, E. V.

doi:10.1109/dd.2015.7354832

Cited by 2 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This problem was considered in [8] for the simplest case k = 1. In this paper we discuss the case k = 2.…”

Section: Introductionmentioning

confidence: 99%

Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials

Borzov¹,

Damaskinsky²

2015

Preprint

Self Cite

View full text Add to dashboard Cite

Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomialsWe consider two families of polynomialsorthogonal on the real line with respect to probability measures µ and ν respectively. Let {Q n (x)} ∞ n=0 and {P n (x)} ∞ n=0 connected by the linear relationsLet us denote A P and A Q generalized oscillator algebras associated with the sequences P and Q. In the case k = 2 we describe all pairs (P,Q), for which the algebras A P and A Q are equal. In addition, we construct corresponding algebras of generalized oscillators for arbitrary k ≥ 1.

show abstract

“…This problem was considered in [8] for the simplest case k = 1. In this paper we discuss the case k = 2.…”

Section: Introductionmentioning

confidence: 99%

Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials

Borzov¹,

Damaskinsky²

2015

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…В настоящей работе исследуется вопрос, при каких условиях алгебры A P и A Q , порождаемые такими линейно-связанными полиномами, совпадают, A P = A Q . Эта задача в простейшем случае k = 1 рассматривалась в работе [7]. В настоящей работе мы обсудим случай k = 2.…”

unclassified

Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials

Borzov¹,

Damaskinskii²,

Damaskinsky³

2017

TMF

View full text Add to dashboard Cite

Рассматриваются семейства многочленов $\mathbb P=\{P_n(x)\}_{n=0}^\infty$ и $\mathbb Q=\{Q_n(x)\}_{n=0}^\infty$, ортогональных на вещественной прямой относительно вероятностных мер $\mu$ и $\nu$ соответственно. Предполагается, что многочлены $\{Q_n(x)\}_{n=0}^\infty$ и $\{P_n(x)\}_{n=0}^\infty$ связаны линейным соотношением. В случае $k=2$ описаны все пары ($\mathbb P$, $\mathbb Q$), для которых совпадают алгебры $\mathfrak A_P$ и $\mathfrak A_Q$ обобщенных осцилляторов, порождаемые $\{Q_n(x)\}_{n=0}^\infty$ и $\{P_n(x)\}_{n=0}^\infty$. Построены алгебры обобщенных осцилляторов, соответствующие парам ($\mathbb P$, $\mathbb Q$) для произвольного $k\geq 1$.

show abstract

On representations of generalized oscillator for two sequences of linearly related orthogonal polynomials

Cited by 2 publications

References 8 publications

Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials

Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials

Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials

Contact Info

Product

Resources

About