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On Some Special Cases of Gaiotto's Positivity Conjecture
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove a conjecture of D. Gaiotto on positivity of inner products arising in studying Landau–Ginzburg boundary conditions in the 1-dimensional case, and in special cases in higher dimensions, for 3d free hypermultiplets.
Keywords: gauge theory, total positivity, positive definite function, Bochner's theorem. 
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     author = {Pavel Etingof},
     title = {On {Some} {Special} {Cases} of {Gaiotto's} {Positivity} {Conjecture}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a62/}
}
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Pavel Etingof. On Some Special Cases of Gaiotto's Positivity Conjecture. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a62/

[1] Gaiotto D., Sphere quantization of Higgs and Coulomb branches and analytic symplectic duality, arXiv: 2307.12396

[2] Gantmacher F.R., The theory of matrices, v. 2, Chelsea Publishing Co., New York, 1959 | MR

[3] Gröchenig K., “Schoenberg's theory of totally positive functions and the Riemann zeta function”, Sampling, Approximation, and Signal Analysis. Harmonic Analysis in the Spirit of J Rowland Higgins, Appl. Numer. Harmon. Anal., Birkhäuser, Cham, 2023, arXiv: 2007.12889 | DOI | MR

[4] Karlin S., “Total positivity, absorption probabilities and applications”, Trans. Amer. Math. Soc., 111 (1964), 33–107 | DOI | MR | Zbl

[5] Karlin S., Total positivity, v. I, Stanford University Press, Stanford, CA, 1968 | MR | Zbl

[6] Rid M., Simon B., Methods of modern mathematical physics, v. II, Academic Press, New York, 1975 | MR

[7] Schoenberg I.J., “On Pólya frequency functions. I The totally positive functions and their Laplace transforms”, J. Anal. Math., 1 (1951), 331–374 | DOI | MR | Zbl