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Topic · Applied Mathematics

Mathematical Analysis and Transform Methods

Mathematical Analysis and Transform Methods is a research topic within Applied Mathematics. Science Explorer counts 16k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers explores advances in the analysis and applications of the Fractional Fourier Transform, including topics such as frames, wavelets, sampling, signal processing, shearlets, modulation spaces, Gabor frames, uncertainty principles, Dunkl transform, and spectral measures.

  • Frames
  • Wavelets
  • Sampling
  • Signal Processing
  • Shearlets
  • Modulation Spaces
  • Gabor Frames
  • Uncertainty Principles
  • Dunkl Transform
  • Spectral Measures
Research works
16k
fractional, since 1950
In the world top 10%
1.6k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+22%
the tick is no change
Largest producer
China
30% of the 10 largest, 2022-now
Mathematical Analysis and Transform Methods

Which countries lead Mathematical Analysis and Transform Methods research?

By volume, China and India publish the most (499 and 286 works in 2022-now).

By volume, 2022-now

  1. 1 China 499 works
  2. 2 India 286 works
  3. 3 United States 248 works
  4. 4 Russia 156 works
  5. 5 Germany 95 works
  6. 6 Italy 94 works
  7. 7 Morocco 86 works
  8. 8 France 77 works
  9. 9 Japan 63 works
  10. 10 Türkiye 57 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 30.0%India: 17.2%United States: 14.9%Russia: 9.4%6 others listed: 28.4%30%largest
China499 · 30.0%India286 · 17.2%United States248 · 14.9%Russia156 · 9.4%6 others listed472 · 28.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Mathematical Analysis and Transform Methods research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Mathematical Analysis and Transform Methods research, followed by Centre National de la Recherche Scientifique and University of Hassan II Casablanca.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 38 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 35 works
  3. 3 University of Hassan II CasablancaMorocco 30 works
  4. 4 University of ViennaAustria 19 works
  5. 5 University of DelhiIndia 18 works
  6. 6 St Petersburg UniversityRussia 18 works
  7. 7 Ghent UniversityBelgium 16 works
  8. 8 Banaras Hindu UniversityIndia 16 works
  9. 9 Université Ibn-TofailMorocco 15 works
  10. 10 Beijing Institute of TechnologyChina 14 works

Who are the leading researchers in Mathematical Analysis and Transform Methods?

The most-cited researchers publishing on Mathematical Analysis and Transform Methods include Kai You Wang, R. W. L. Jones and H. Vincent Poor.

  1. 1 Kai You Wang China 224k citations
  2. 2 R. W. L. Jones United Kingdom 189k citations
  3. 3 H. Vincent Poor United States 165k citations
  4. 4 Anil Kumar Jain United States 160k citations
  5. 5 David L. Donoho United States 154k citations
  6. 6 Alan Conrad Bovik United States 150k citations
  7. 7 Stephen Boyd United States 142k citations
  8. 8 B. Allen Germany 134k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Mathematical Analysis and Transform Methods?

The most cited paper in Mathematical Analysis and Transform Methods is "Compressed sensing" (David L. Donoho, 2006), with 23,533 citations. Next come "A Practical Guide to Wavelet Analysis" (15,178) and "Matching pursuits with time-frequency dictionaries" (9,224).

Most cited papers
#PaperReleasedCitations
1 Compressed sensing David L. Donoho · IEEE Transactions on Information Theory Apr 2006 23,533
2 A Practical Guide to Wavelet Analysis Christopher Torrence, Gilbert P. Compo · Bulletin of the American Meteorological Society Open access 1998 15,178
3 Matching pursuits with time-frequency dictionaries Stéphane Mallat, Zhifeng Zhang · IEEE Transactions on Signal Processing 1993 9,224
4 Orthonormal bases of compactly supported wavelets Ingrid C. Daubechies · Communications on Pure and Applied Mathematics Oct 1988 8,242
5 Stable signal recovery from incomplete and inaccurate measurements Emmanuel J. Candès, Justin Romberg, Terence Tao · Communications on Pure and Applied Mathematics Mar 2006 7,249
All 100 most cited papers, with filters and sorting

Where is Mathematical Analysis and Transform Methods research done?

The largest centres of Mathematical Analysis and Transform Methods research in 2022-now are Beijing (China), Moscow (Russia), Vienna (Austria) and New Delhi (India). Among places with at least 20 works in it, it is an unusually large share of all research in Casablanca, Srinagar and Tunis.

Largest cities, 2022-now

  1. 1 BeijingChina 85 works
  2. 2 MoscowRussia 60 works
  3. 3 ViennaAustria 33 works
  4. 4 New DelhiIndia 32 works
  5. 5 CasablancaMorocco 30 works
  6. 6 TunisTunisia 29 works
  7. 7 GuangzhouChina 28 works
  8. 8 NanjingChina 28 works
  9. 9 SrinagarIndia 24 works
  10. 10 VaranasiIndia 24 works

Where it is the local speciality

  1. CasablancaMA · 29.9 works25×
  2. SrinagarIN · 24.5 works23×
  3. TunisTN · 29.3 works18×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Mathematical Analysis and Transform Methods than the world average.

See Mathematical Analysis and Transform Methods on the map

Where is the best place to study Mathematical Analysis and Transform Methods?

Among universities, judged by research, Islamic University of Science and Technology, Politecnico di Milano and University of Hassan II Casablanca score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 22.81%fractional works in this field (log) →share of work in the world top 10% →Politecnico di MilanoIslamic University o…University of ViennaUniversity of Hassan…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Islamic University of Science and TechnologyIndia 71.237.5%168.9×12 +517.6%
2Politecnico di MilanoItaly 61.639.5%6.8×11 +99.7%
3University of Hassan II CasablancaMorocco 60.810.4%53.0×30 +77.3%
4University of ViennaAustria 59.811.0%17.6×20 +107.7%
5Indian Institute of Technology DhanbadIndia 58.426.1%31.1×14 +60.4%
6University of KashmirIndia 57.121.9%33.4×13 +77.9%
7Taibah UniversitySaudi Arabia 56.120.7%35.3×12 +37.9%
8Beijing Institute of TechnologyChina 51.932.1%5.6×14 -10.3%
9Ghent UniversityBelgium 50.88.3%9.6×16 +26.7%
10Beijing Normal UniversityChina 46.220.6%7.2×12 +10.1%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Mathematical Analysis and Transform Methods, country by country

Is Mathematical Analysis and Transform Methods research growing?

Output in 2022-2025 was 22% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Mathematical Analysis and Transform Methods.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Mathematical Analysis and Transform Methods as a percentage of every work published that year, 0.012% in 2024.

still counting0.010%0.020%0.030%Mathematical Analysis and Transform Methods0.011% in 202519801990200020102020

Fractional works of Mathematical Analysis and Transform Methods over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Mathematical Analysis and Transform Methods10.1% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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