H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 32 Citations 6,032 64 World Ranking 1809 National Ranking 777

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Algebra
  • Hilbert space

His main research concerns Mathematical analysis, Wavelet, Atomic decomposition, Banach space and Combinatorics. The study incorporates disciplines such as Abelian group and Scalar in addition to Mathematical analysis. His biological study spans a wide range of topics, including Discrete mathematics, Algorithm and Signal processing.

His Banach space research is under the purview of Pure mathematics. His Pure mathematics research is multidisciplinary, relying on both Basis and Gabor–Wigner transform. As part of one scientific family, Christopher Heil deals mainly with the area of Combinatorics, narrowing it down to issues related to the Gabor frame, and often Function and Tight frame.

His most cited work include:

  • Continuous and discrete wavelet transforms (945 citations)
  • The application of multiwavelet filterbanks to image processing (404 citations)
  • A basis theory primer (207 citations)

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

Pure mathematics, Mathematical analysis, Wavelet, Algebra and Orthonormal basis are his primary areas of study. His work in Pure mathematics covers topics such as Balian–Low theorem which are related to areas like Zak transform, M. Riesz extension theorem, Gabor wavelet, Tight frame and Gabor frame. Christopher Heil combines subjects such as Function, Structure, Combinatorics and Joint spectral radius with his study of Mathematical analysis.

The concepts of his Wavelet study are interwoven with issues in Algorithm and Microlocal analysis. His Algebra study combines topics from a wide range of disciplines, such as Compact operator and Conjecture. His Modulation space research incorporates themes from Gabor–Wigner transform and Discrete mathematics.

He most often published in these fields:

  • Pure mathematics (44.64%)
  • Mathematical analysis (28.57%)
  • Wavelet (25.89%)

What were the highlights of his more recent work (between 2011-2019)?

  • Pure mathematics (44.64%)
  • Algebra (16.96%)
  • Hilbert space (10.71%)

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

Christopher Heil mostly deals with Pure mathematics, Algebra, Hilbert space, Metric space and Space. The various areas that Christopher Heil examines in his Pure mathematics study include Orthonormal basis and Matrix. His Algebra study integrates concerns from other disciplines, such as Zero divisor and Time–frequency analysis.

His study looks at the intersection of Hilbert space and topics like Product with Orthogonality. Christopher Heil studied Metric space and Banach space that intersect with Norm. Christopher Heil interconnects Modulation space, Zak transform and Balian–Low theorem in the investigation of issues within Space.

Between 2011 and 2019, his most popular works were:

  • WHAT IS... a Frame (17 citations)
  • The HRT Conjecture and the Zero Divisor Conjecture for the Heisenberg Group (11 citations)
  • Duals of Weighted Exponential Systems (5 citations)

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

  • Mathematical analysis
  • Algebra
  • Hilbert space

His primary scientific interests are in Pure mathematics, Artificial intelligence, Real analysis, Real-time computing and Computer vision. His work deals with themes such as Space, Balian–Low theorem and Zak transform, which intersect with Pure mathematics.

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.

Top Publications

Continuous and discrete wavelet transforms

C. Heil;D. F. Walnut.
Siam Review (1989)

1479 Citations

The application of multiwavelet filterbanks to image processing

V. Strela;P.N. Heller;G. Strang;P. Topiwala.
IEEE Transactions on Image Processing (1999)

786 Citations

A basis theory primer

Christopher Heil.
(2011)

308 Citations

History and Evolution of the Density Theorem for Gabor Frames

Christopher Heil.
Journal of Fourier Analysis and Applications (2007)

243 Citations

MODULATION SPACES AND PSEUDODIFFERENTIAL OPERATORS

Karlheinz Gröchenig;Christopher Heil.
Integral Equations and Operator Theory (1999)

239 Citations

Approximation by translates of refinable functions

Christopher Heil;Gilbert Strang;Vasily Strela.
Numerische Mathematik (1996)

236 Citations

Density of Gabor Frames

Ole Christensen;Baiqiao Deng;Christopher Heil.
Applied and Computational Harmonic Analysis (1999)

230 Citations

Differentiation and the Balian-Low Theorem

John J. Benedetto;Christopher Heil;David F. Walnut.
Journal of Fourier Analysis and Applications (1994)

226 Citations

Perturbations of Banach Frames and Atomic Decompositions

Oel Christensen;Christopher Heil.
Mathematische Nachrichten (2009)

195 Citations

An Introduction to Weighted Wiener Amalgams

Christopher Heil.
(2003)

177 Citations

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

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