Analysis — Open Conjectures

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Includes conjectures from complex analysis, harmonic analysis, functional analysis, and operator theory.

Complex Analysis

# Conjecture Eponym(s) Comments
1 Brennan conjecture James E. Brennan  
2 Sendov’s conjecture Blagovest Sendov Concerns complex polynomials

Harmonic Analysis

# Conjecture Eponym(s) Comments
1 Bochner–Riesz conjecture Salomon Bochner, Marcel Riesz ⇒ restriction conjecture ⇒ Kakeya maximal function conjecture ⇒ Kakeya dimension conjecture

Functional Analysis

# Conjecture Eponym(s) Comments
1 Invariant subspace problem —  

Operator Theory

# Conjecture Eponym(s) Comments
1 Baum–Connes conjecture Paul Baum, Alain Connes Operator K-theory. ⇒ Gromov-Lawson-Rosenberg conjecture; ⇒ Kaplansky-Kadison conjecture; ⇒ Novikov conjecture
2 Zauner’s conjecture Gerhard Zauner  

References

  • Stein, E. M. & Shakarchi, R. Princeton Lectures in Analysis. Vols. I–IV, Princeton University Press.
  • Conway, J. B. A Course in Functional Analysis. 2nd ed., Springer GTM 96.

See also the centralized bibliography for general references.