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 33 Citations 4,867 295 World Ranking 1689 National Ranking 737

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Hilbert space
  • Algebra

Daniel Alpay mainly investigates Algebra, Pure mathematics, Mathematical analysis, Hilbert space and Space. His Algebra study integrates concerns from other disciplines, such as Schur's theorem and Realization. His work focuses on many connections between Pure mathematics and other disciplines, such as Bounded function, that overlap with his field of interest in Differential operator.

His work in Mathematical analysis tackles topics such as Matrix function which are related to areas like Unit circle, Inverse scattering transform and Inverse scattering problem. The concepts of his Hilbert space study are interwoven with issues in Analytic function, Kernel and Interpolation. In Space, Daniel Alpay works on issues like Quaternion, which are connected to Clifford algebra, Finite set, Scalar and Eigenvalues and eigenvectors.

His most cited work include:

  • Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (174 citations)
  • On Applications of Reproducing Kernel Spaces to the Schur Algorithm and Rational J Unitary Factorization (120 citations)
  • Hilbert spaces of analytic functions, inverse scattering and operator models.II (106 citations)

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

Daniel Alpay mainly focuses on Pure mathematics, Algebra, Mathematical analysis, Hilbert space and Interpolation. The Pure mathematics study combines topics in areas such as Space, Quaternion and Discrete mathematics. The various areas that Daniel Alpay examines in his Algebra study include Operator theory and Schur's theorem.

His Mathematical analysis research is multidisciplinary, incorporating elements of Function and Applied mathematics. His work carried out in the field of Hilbert space brings together such families of science as Analytic function and Kernel. His Interpolation research incorporates elements of Class and Boundary.

He most often published in these fields:

  • Pure mathematics (49.66%)
  • Algebra (25.84%)
  • Mathematical analysis (23.37%)

What were the highlights of his more recent work (between 2017-2021)?

  • Pure mathematics (49.66%)
  • Algebra (25.84%)
  • Quaternion (7.64%)

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

Daniel Alpay mostly deals with Pure mathematics, Algebra, Quaternion, Space and Rational function. He has researched Pure mathematics in several fields, including Variable and Realization. His study in the field of Interpolation and Infinity also crosses realms of Markov chain.

His study in Quaternion is interdisciplinary in nature, drawing from both Complex number, Open unit, Ball and Hypercomplex analysis. His Space research includes themes of Structure, Wiener filter, Banach space and Hilbert space. His studies in Rational function integrate themes in fields like Exterior algebra, Series, Lemma and Inversion.

Between 2017 and 2021, his most popular works were:

  • Quaternionic de Branges Spaces and Characteristic Operator Function (11 citations)
  • On Slice Polyanalytic Functions of a Quaternionic Variable (11 citations)
  • Herglotz functions of several quaternionic variables (7 citations)

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

  • Mathematical analysis
  • Hilbert space
  • Algebra

Daniel Alpay spends much of his time researching Pure mathematics, Rational function, Quaternion, Algebra and Space. In his research, Daniel Alpay performs multidisciplinary study on Pure mathematics and Fock space. His research ties Wavelet and Algebra together.

His Space research incorporates themes from Structure and Combinatorics. His research investigates the connection with Unit sphere and areas like Class which intersect with concerns in Interpolation. His Kernel research focuses on Function and how it relates to Realization.

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

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Daniel Alpay.
(1997)

296 Citations

On Applications of Reproducing Kernel Spaces to the Schur Algorithm and Rational J Unitary Factorization

Daniel Alpay;Harry Dym.
(1986)

147 Citations

The Schur Algorithm, Reproducing Kernel Spaces and System Theory

Daniel Alpay.
(2001)

136 Citations

Unitary Rational Matrix Functions

Daniel Alpay;Israel Gohberg.
(1988)

128 Citations

Reproducing Kernel Spaces and Applications

Daniel Alpay;Fabrizio Colombo;Irene Sabadini.
(2003)

124 Citations

Hilbert spaces of analytic functions, inverse scattering and operator models.II

Daniel Alpay;Harry Dym.
Integral Equations and Operator Theory (1984)

117 Citations

Lossless Inverse Scattering and Reproducing Kernels for Upper Triangular Operators

Daniel Alpay;Patrick Dewilde;Harry Dym.
(1990)

96 Citations

Slice Hyperholomorphic Schur Analysis

Daniel Alpay;Fabrizio Colombo;Irene Sabadini.
(2016)

92 Citations

Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions

Daniel Alpay;Fabrizio Colombo;Irene Sabadini.
Journal D Analyse Mathematique (2013)

84 Citations

Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting

Daniel Alpay;Fabrizio Colombo;Irene Sabadini.
Integral Equations and Operator Theory (2012)

83 Citations

Editorial Boards

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Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

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