D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 38 Citations 5,317 156 World Ranking 1172 National Ranking 59

Overview

What is he best known for?

The fields of study he is best known for:

  • Algebra
  • Quantum mechanics
  • Mathematical analysis

His primary scientific interests are in Pure mathematics, Orthogonal polynomials, Algebra, Jacobi polynomials and Classical orthogonal polynomials. His Pure mathematics study combines topics from a wide range of disciplines, such as Discrete mathematics and Generalization. His research in Orthogonal polynomials intersects with topics in Simple and Recurrence relation.

The study incorporates disciplines such as Hopf algebra, Algebra over a field, Filtered algebra and Cellular algebra in addition to Algebra. His work carried out in the field of Jacobi polynomials brings together such families of science as Differential operator and Eigenvalues and eigenvectors. His work deals with themes such as Hahn polynomials, Closure and Schrödinger's cat, which intersect with Discrete orthogonal polynomials.

His most cited work include:

  • A 'missing' family of classical orthogonal polynomials (292 citations)
  • “Hidden symmetry” of Askey-Wilson polynomials (205 citations)
  • Mutual integrability, quadratic algebras, and dynamical symmetry (193 citations)

What are the main themes of his work throughout his whole career to date?

Alexei Zhedanov mostly deals with Orthogonal polynomials, Pure mathematics, Algebra, Classical orthogonal polynomials and Jacobi polynomials. His study in Orthogonal polynomials concentrates on Discrete orthogonal polynomials, Wilson polynomials, Hahn polynomials, Difference polynomials and Gegenbauer polynomials. The Hahn polynomials study combines topics in areas such as Kravchuk polynomials and Meixner polynomials.

His Pure mathematics research incorporates themes from Recurrence relation, Quadratic equation, Orthogonality and Generalization. His Algebra research includes themes of Algebra over a field and Filtered algebra. His Jacobi polynomials study deals with Eigenvalues and eigenvectors intersecting with Differential operator.

He most often published in these fields:

  • Orthogonal polynomials (46.56%)
  • Pure mathematics (42.51%)
  • Algebra (34.41%)

What were the highlights of his more recent work (between 2015-2021)?

  • Pure mathematics (42.51%)
  • Algebra (34.41%)
  • Orthogonal polynomials (46.56%)

In recent papers he was focusing on the following fields of study:

Alexei Zhedanov mainly investigates Pure mathematics, Algebra, Orthogonal polynomials, Quadratic equation and Algebra over a field. His Pure mathematics study combines topics from a wide range of disciplines, such as Type and Algebraic number. Classical orthogonal polynomials is the focus of his Orthogonal polynomials research.

His studies deal with areas such as Isospectral and Inverse problem as well as Classical orthogonal polynomials. His research investigates the link between Quadratic equation and topics such as Truncation that cross with problems in Limit. His Algebra over a field research is multidisciplinary, incorporating elements of Embedding and Jacobi polynomials.

Between 2015 and 2021, his most popular works were:

  • Quantum spin chains with fractional revival (35 citations)
  • Tridiagonalization and the Heun equation (35 citations)
  • Algebraic Heun Operator and Band-Time Limiting (30 citations)

In his most recent research, the most cited papers focused on:

  • Algebra
  • Quantum mechanics
  • Mathematical analysis

Alexei Zhedanov spends much of his time researching Algebra, Orthogonal polynomials, Pure mathematics, Algebra over a field and Quadratic equation. His Centralizer and normalizer study, which is part of a larger body of work in Algebra, is frequently linked to Duality, bridging the gap between disciplines. His Orthogonal polynomials research includes themes of Mathematical Operators and Quantum mechanics, Spin-½.

His Pure mathematics study integrates concerns from other disciplines, such as Orthogonality, Type, Separation of variables, Quantum and Generalization. His Algebra over a field research is multidisciplinary, incorporating perspectives in Askey–Wilson polynomials and Algebraic number. The various areas that Alexei Zhedanov examines in his Quadratic equation study include Truncation, Hypergeometric function, Wilson polynomials, Recurrence relation and Magnetic field.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

A 'missing' family of classical orthogonal polynomials

Luc Vinet;Alexei Zhedanov.
Journal of Physics A (2011)

292 Citations

“Hidden symmetry” of Askey-Wilson polynomials

A. S. Zhedanov.
Theoretical and Mathematical Physics (1991)

217 Citations

Rational spectral transformations and orthogonal polynomials

Alexei Zhedanov.
Journal of Computational and Applied Mathematics (1997)

203 Citations

Mutual integrability, quadratic algebras, and dynamical symmetry

Ya.I Granovskii;I.M Lutzenko;A.S Zhedanov.
Annals of Physics (1992)

193 Citations

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations

Ryu Sasaki;Satoshi Tsujimoto;Alexei Zhedanov.
Journal of Physics A (2010)

161 Citations

Quadratic algebra as a 'hidden' symmetry of the Hartmann potential

Y I Granovskii;A S Zhedanov;I M Lutzenko.
Journal of Physics A (1991)

122 Citations

Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials

Vyacheslav Spiridonov;Alexei Zhedanov.
Methods and applications of analysis (1994)

121 Citations

Spectral Transformation Chains and Some New Biorthogonal Rational Functions

Vyacheslav Spiridonov;Alexei Zhedanov.
Communications in Mathematical Physics (2000)

118 Citations

Regular Article: Biorthogonal Rational Functions and the Generalized Eigenvalue Problem

Alexei Zhedanov.
Journal of Approximation Theory (1999)

112 Citations

Dunkl shift operators and Bannai–Ito polynomials

Satoshi Tsujimoto;Luc Vinet;Alexei Zhedanov.
Advances in Mathematics (2012)

106 Citations

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Best Scientists Citing Alexei Zhedanov

Luc Vinet

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Eric M. Rains

California Institute of Technology

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