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Topic · Applied Mathematics

Holomorphic and Operator Theory

Holomorphic and Operator Theory is a research topic within Applied Mathematics. Science Explorer counts 23k research works in it since 1950. 11.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics in complex analysis and operator theory, including composition operators, weighted spaces, Toeplitz operators, hypercyclic operators, Bergman spaces, holomorphic functions, Nevanlinna–Pick kernels, operator theory, function theory, and spectral factorization.

  • Composition Operators
  • Weighted Spaces
  • Toeplitz Operators
  • Hypercyclic Operators
  • Bergman Spaces
  • Holomorphic Functions
  • Nevanlinna–Pick Kernels
  • Operator Theory
  • Function Theory
  • Spectral Factorization
Research works
23k
fractional, since 1950
In the world top 10%
2.5k
per year above
Top-10% rate
11.2%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+5%
the tick is no change

Which countries lead Holomorphic and Operator Theory research?

By volume, China and India publish the most (529 and 314 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 529 works
  2. 2 India 314 works
  3. 3 United States 271 works
  4. 4 Russia 197 works
  5. 5 Spain 99 works
  6. 6 France 98 works
  7. 7 Türkiye 95 works
  8. 8 Germany 89 works
  9. 9 Iran 83 works
  10. 10 Japan 81 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: 28.5%India: 16.9%United States: 14.6%Russia: 10.6%6 others listed: 29.4%28%largest
China529 · 28.5%India314 · 16.9%United States271 · 14.6%Russia197 · 10.6%6 others listed546 · 29.4%

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

Which institutions lead Holomorphic and Operator Theory research?

By volume in 2022–2025, University of Sfax publishes the most Holomorphic and Operator Theory research, followed by Lomonosov Moscow State University and University of Delhi.

By volume, 2022–2025

  1. 1 University of SfaxTunisia 31 works
  2. 2 Lomonosov Moscow State UniversityRussia 23 works
  3. 3 University of DelhiIndia 19 works
  4. 4 Indian Institute of Science BangaloreIndia 18 works
  5. 5 University of NisSerbia 14 works
  6. 6 Indian Statistical InstituteIndia 14 works
  7. 7 Jadavpur UniversityIndia 14 works
  8. 8 Centre National de la Recherche ScientifiqueFrance 14 works
  9. 9 King Saud UniversitySaudi Arabia 14 works
  10. 10 University of BelgradeSerbia 14 works

Who are the leading researchers in Holomorphic and Operator Theory?

The most-cited researchers publishing on Holomorphic and Operator Theory include Stephan Ramon Garcia.

  1. 1 Stephan Ramon Garcia United States 4k citations

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

Where is Holomorphic and Operator Theory research done?

The largest centres of Holomorphic and Operator Theory research in 2022–2025 are Moscow (Russia), Beijing (China), New Delhi (India) and Guangzhou (China). Among places with at least 20 works in it, it is an unusually large share of all research in Sfax.

Largest cities, 2022–2025

  1. 1 Moscow Russia 75 works
  2. 2 Beijing China 54 works
  3. 3 New Delhi India 40 works
  4. 4 Guangzhou China 39 works
  5. 5 Kolkata India 38 works
  6. 6 Shanghai China 35 works
  7. 7 Sfax Tunisia 31 works
  8. 8 Tianjin China 28 works
  9. 9 Seoul South Korea 28 works
  10. 10 Hanoi Vietnam 26 works

Where it is the local speciality

  1. SfaxTN · 31.1 works26×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Holomorphic and Operator Theory than the world average.

See Holomorphic and Operator Theory on the map

Where is the best place to study Holomorphic and Operator Theory?

Among universities, judged by research, Jadavpur University, University of Sfax and Chouaib Doukkali University 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 25.31%fractional works in this node (log) →share in the world top 10% →Jadavpur University: 14, 43.4%University of Sfax: 31, 5.2%Chouaib Doukkali University: 9, 41.9%University of Nis: 14, 16.8%University of Oradea: 8, 43.7%Delhi Technological University: 10, 33.6%Indian Institute of Science Bangalore: 18, 20.7%Lomonosov Moscow State University: 22, 9.0%Babeș-Bolyai University: 10, 22.7%University of Al-Qadisiyah: 12, 16.1%Jadavpur UniversityChouaib Doukkali Uni…University of NisUniversity of Sfax
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1 Jadavpur UniversityIndia 70.143.4%16.9×14 —
2 University of SfaxTunisia 68.45.2%39.5×31 +198.1%
3 Chouaib Doukkali UniversityMorocco 63.841.9%30.9×9 —
4 University of NisSerbia 62.416.8%27.6×14 +206.6%
5 University of OradeaRomania 59.243.7%30.9×8 -20.2%
6 Delhi Technological UniversityIndia 56.633.6%11.5×10 —
7 Indian Institute of Science BangaloreIndia 54.820.7%14.9×18 -22.9%
8 Lomonosov Moscow State UniversityRussia 53.79.0%8.4×22 +71.2%
9 Babeș-Bolyai UniversityRomania 49.922.7%13.1×10 +26.9%
10 University of Al-QadisiyahIraq 48.516.1%24.6×12 —

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Holomorphic and Operator Theory research growing?

Output in 2018–2022 was 5% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Holomorphic and Operator Theory.

19801990200020102020
grewheldshrank

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

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.