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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. 10.1% 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%
2.3k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+19%
the tick is no change
Largest producer
China
28% of the 10 largest, 2022-now
Holomorphic and Operator Theory

Which countries lead Holomorphic and Operator Theory research?

By volume, China and India publish the most (663 and 392 works in 2022-now).

By volume, 2022-now

  1. 1 China 663 works
  2. 2 India 392 works
  3. 3 United States 362 works
  4. 4 Russia 248 works
  5. 5 France 128 works
  6. 6 Spain 123 works
  7. 7 Germany 114 works
  8. 8 Türkiye 111 works
  9. 9 Japan 102 works
  10. 10 Italy 96 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: 28.3%India: 16.8%United States: 15.5%Russia: 10.6%6 others listed: 28.8%28%largest
China663 · 28.3%India392 · 16.8%United States362 · 15.5%Russia248 · 10.6%6 others listed673 · 28.8%

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

Which institutions lead Holomorphic and Operator Theory research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Holomorphic and Operator Theory research, followed by Centre National de la Recherche Scientifique and University of Sfax.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 69 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 63 works
  3. 3 University of SfaxTunisia 35 works
  4. 4 Lomonosov Moscow State UniversityRussia 28 works
  5. 5 National Academy of Sciences of UkraineUkraine 26 works
  6. 6 University of DelhiIndia 23 works
  7. 7 Indian Institute of Science BangaloreIndia 20 works
  8. 8 King Saud UniversitySaudi Arabia 17 works
  9. 9 Jadavpur UniversityIndia 16 works
  10. 10 University of NisSerbia 16 works

Who are the leading researchers in Holomorphic and Operator Theory?

The most-cited researchers publishing on Holomorphic and Operator Theory include Edward H. Witten, J. Conway and Stanley Osher.

  1. 1 Edward H. Witten United States 174k citations
  2. 2 J. Conway Germany 139k citations
  3. 3 Stanley Osher United States 119k 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 Holomorphic and Operator Theory?

The most cited paper in Holomorphic and Operator Theory is "LOSS OF RECENT MEMORY AFTER BILATERAL HIPPOCAMPAL LESIONS" (William Beecher Scoville, Brenda Atkinson Milner, 1957), with 7,447 citations. Next come "Hp spaces of several variables" (2,887) and "Completely positive linear maps on complex matrices" (2,767).

Most cited papers
#PaperReleasedCitations
1 LOSS OF RECENT MEMORY AFTER BILATERAL HIPPOCAMPAL LESIONS William Beecher Scoville, Brenda Atkinson Milner · Journal of Neurology Neurosurgery & Psychiatry Open access Feb 1957 7,447
2 Hp spaces of several variables Charles Fefferman, E. M. Stein · Acta Mathematica 1972 2,887
3 Completely positive linear maps on complex matrices Man-Duen Choi · Linear Algebra and its Applications Open access Jun 1975 2,767
4 Weighted norm inequalities for the Hardy maximal function Benjamin Muckenhoupt · Transactions of the American Mathematical Society Open access 1972 1,738
5 Vector-valued laplace transforms and cauchy problems Wolfgang Arendt · Israel Journal of Mathematics Oct 1987 1,437
All 99 most cited papers, with filters and sorting

Where is Holomorphic and Operator Theory research done?

The largest centres of Holomorphic and Operator Theory research in 2022-now 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-now

  1. 1 MoscowRussia 96 works
  2. 2 BeijingChina 68 works
  3. 3 New DelhiIndia 48 works
  4. 4 GuangzhouChina 47 works
  5. 5 ShanghaiChina 43 works
  6. 6 KolkataIndia 42 works
  7. 7 SeoulSouth Korea 37 works
  8. 8 SfaxTunisia 35 works
  9. 9 TianjinChina 34 works
  10. 10 HanoiVietnam 32 works

Where it is the local speciality

  1. SfaxTN · 34.9 works24×
← 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 Jordan and University of Sfax 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%60%mean 23.36%fractional works in this field (log) →share of work in the world top 10% →University of JordanJadavpur UniversityUniversity of SfaxLomonosov Moscow Sta…
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
1Jadavpur UniversityIndia 69.142.9%16.5×16 +418.8%
2University of JordanJordan 64.847.7%9.2×9 +226.5%
3University of SfaxTunisia 62.710.8%40.7×35 +73.1%
4Lomonosov Moscow State UniversityRussia 52.78.3%9.6×28 +28.8%
5Indian Institute of Science BangaloreIndia 50.618.3%14.6×20 +160.7%
6Chouaib Doukkali UniversityMorocco 49.930.9%31.6×10 +273.9%
7Politecnico di MilanoItaly 48.028.8%4.7×12 +28.7%
8University of NisSerbia 47.816.3%27.4×16 +79.6%
9King Saud UniversitySaudi Arabia 46.315.2%5.0×17 +125.0%
10University of Al-QadisiyahIraq 46.014.4%29.8×16 +29.5%

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 Holomorphic and Operator Theory, country by country

Is Holomorphic and Operator Theory research growing?

Output in 2022-2025 was 19% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Holomorphic and Operator Theory.

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 Holomorphic and Operator Theory as a percentage of every work published that year, 0.015% in 2024.

still counting0.020%0.040%0.060%Holomorphic and Operator Theory0.017% in 202519801990200020102020

Fractional works of Holomorphic and Operator Theory 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%Holomorphic and Operator Theory9.9% 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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