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Mathematics

D-Index
39
Citations
6590
World Ranking
2199
National Ranking
929

Overview

Daniel Alpay is affiliated with Chapman University in the United States and specializes primarily in mathematics with a focus on applied mathematics and its related subfields. Their research spans a wide array of mathematical topics, including applied mathematics, mathematical physics, computational theory and mathematics, statistical and nonlinear physics, and geometry and topology.

Their main topics of work cover diverse areas such as algebraic and geometric analysis, mathematical analysis and transform methods, holomorphic and operator theory, matrix theory and algorithms, advanced topics in algebra, mathematical functions and polynomials, and various applications of mathematics.

Daniel Alpay has contributed to numerous publications and is frequently published in venues such as arXiv (Cornell University), Linear Algebra and its Applications, Virtual Community of Pathological Anatomy (University of Castilla La Mancha), Integral Equations and Operator Theory, and Opuscula Mathematica.

Selected recent papers include:

  • On the global operator and Fueter mapping theorem for slice polyanalytic functions, 2021, Virtual Community of Pathological Anatomy (University of Castilla La Mancha)
  • Operators induced by certain hypercomplex systems, 2023, Opuscula Mathematica
  • Correction to: On Slice Polyanalytic Functions of a Quaternionic Variable, 2021, Results in Mathematics
  • Short-time Fourier transform and superoscillations, 2024, Applied and Computational Harmonic Analysis
  • Infinite-order Differential Operators Acting on Entire Hyperholomorphic Functions, 2021, Virtual Community of Pathological Anatomy (University of Castilla La Mancha)

They have frequently collaborated with researchers such as Irene Sabadini, Fabrizio Colombo, Kamal Diki, Mihaela Vajiac, and Ilwoo Cho.

In terms of book publications, Daniel Alpay has works published by Springer Nature, Springer International Publishing, and Chapman mathematical notes. Notable titles include:

  • Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions (2024)
  • Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory (2020)
  • New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative (2021)
  • Quaternionic de Branges Spaces and Characteristic Operator Function (2020)
  • Exercises in Applied Mathematics (2024)

Best Publications

  • Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

    D Alpay;Aad Dijksma;J Rovnyak;H deSnoo

  • Slice Hyperholomorphic Schur Analysis

    Daniel Alpay;Fabrizio Colombo;Irene Sabadini

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

    Daniel Alpay;Harry Dym

  • Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

    Daniel Alpay;Maria Elena Luna-Elizarrarás;Michael Shapiro;Daniele Carlo Struppa

  • The Schur Algorithm, Reproducing Kernel Spaces and System Theory

    Daniel Alpay

  • Unitary Rational Matrix Functions

    Daniel Alpay;Israel Gohberg

  • The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

    Daniel Alpay;Fabrizio Colombo;David P. Kimsey

  • Reproducing Kernel Spaces and Applications

    Daniel Alpay;Fabrizio Colombo;Irene Sabadini

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

    Daniel Alpay;Harry Dym

  • Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting

    Daniel Alpay;Fabrizio Colombo;Irene Sabadini

  • Lossless Inverse Scattering and Reproducing Kernels for Upper Triangular Operators

    Daniel Alpay;Patrick Dewilde;Harry Dym

  • Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions

    Daniel Alpay;Fabrizio Colombo;Irene Sabadini

  • On a New Class of Structured Reproducing Kernel Spaces

    Daniel Alpay;H. Dym

  • INTERPOLATION PROBLEMS, EXTENSIONS OF SYMMETRICAL OPERATORS AND REPRODUCING KERNEL SPACES II

    Daniel Alpay;A Dijksma;H de Snoo

  • Reproducing Kernel Quaternionic Pontryagin Spaces

    Daniel Alpay;Michael Shapiro

  • The Fock Space in the Slice Hyperholomorphic Setting

    Daniel Alpay;Fabrizio Colombo;Irene Sabadini;Guy Salomon

  • Krein–Langer Factorization and Related Topics in the Slice Hyperholomorphic Setting

    Daniel Alpay;Fabrizio Colombo;Irene Sabadini

  • Stochastic Processes Induced By Singular Operators

    Daniel Alpay;Palle E. T. Jorgensen

  • Some extremal problems linked with indentification from partial frequency data

    Daniel Alpay;Laurent Baratchart;Juliette Leblond

  • Algorithme de Schur, espaces à noyau reproduisant et théorie des systèmes

    Daniel Alpay

Frequent Co-Authors

Irene Sabadini
Irene Sabadini Polytechnic University of Milan
Israel Gohberg
Israel Gohberg Tel Aviv University
Palle E. T. Jorgensen
Palle E. T. Jorgensen University of Iowa
Daniele C. Struppa
Daniele C. Struppa Chapman University
Joseph A. Ball
Joseph A. Ball Virginia Tech
Marinus A. Kaashoek
Marinus A. Kaashoek Vrije Universiteit Amsterdam
Philippe Loubaton
Philippe Loubaton Université Paris Cité
Simeon Reich
Simeon Reich Technion – Israel Institute of Technology
Mihai Putinar
Mihai Putinar University of California, Santa Barbara

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