S. Abenda and P. Grinevich, Rational degeneration of M-curves, totally positive Grassmannians and KP-solitons. Preprint https

A. Berenstein, S. Fomin, and A. Zelevinsky, Parametrizations of Canonical Bases and Totally Positive Matrices, Advances in Mathematics, vol.122, issue.1
DOI : 10.1006/aima.1996.0057
URL : https://doi.org/10.1006/aima.1996.0057

A. Berenstein and A. Zelevinsky, Total positivity in Schubert varieties, Commentarii Mathematici Helvetici, vol.72, issue.1, pp.128-166, 1997.
DOI : 10.1007/PL00000363
URL : http://www.ems-ph.org/journals/show_pdf.php?issn=0010-2571&vol=72&iss=1&rank=10

M. Boiti, F. Pempinelli, and A. K. Pogrebkov, Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions, Journal of Mathematical Physics, vol.19, issue.8, p.83506, 2011.
DOI : 10.1090/chel/345
URL : http://arxiv.org/abs/1105.3681

V. M. Buchstaber and A. A. Glutsyuk, On determinants of modified Bessel functions and entire solutions of double confluent Heun equations, Nonlinearity, vol.29, issue.12, pp.29-3857, 2016.
DOI : 10.1088/0951-7715/29/12/3857

V. M. Buchstaber and S. I. Tertychnyi, A remarkable sequence of Bessel matrices, Mathematical Notes, issue.5, pp.98-714, 2015.

S. M. Fallat and C. R. Johnson, Totally nonnegative matrices, 2011.
DOI : 10.1515/9781400839018

S. M. Fallat, C. R. Johnson, and A. D. Sokal, Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples, Linear Algebra and its Applications, vol.520
DOI : 10.1016/j.laa.2017.01.013

S. Fomin and A. Zelevinsky, Double Bruhat cells and total positivity, Journal of the American Mathematical Society, vol.12, issue.02, pp.335-380, 1999.
DOI : 10.1090/S0894-0347-99-00295-7

F. Gantmacher, The theory of matrices, 1959.

F. Gantmacher and M. Krein, Sur les matrices oscillatoires etcompì etement non negatives, Compositio Math, vol.4, pp.445-476, 1937.

F. R. Gantmacher and M. G. Krein, Oscillation matrices and small oscillations of mechanical systems, Russian), 1941.
DOI : 10.1090/chel/345

F. R. Gantmacher and M. G. Krein, Oscillation matrices and kernels and small oscillations of mechanical systems, Russian), 1950.

M. Gasca and C. A. Michelli, Total positivity and its applications Mathematics and its applications, pp.109-130, 1996.

I. M. Gelfand, R. M. Goresky, R. D. Macpherson, and V. Serganova, Combinatorial geometries, convex polyhedra, and schubert cells, Advances in Mathematics, vol.63, issue.3, pp.301-316, 1987.
DOI : 10.1016/0001-8708(87)90059-4
URL : https://doi.org/10.1016/0001-8708(87)90059-4

G. Lusztig, A Survey of Total Positivity, Milan Journal of Mathematics, vol.76, issue.1, pp.125-134, 2008.
DOI : 10.1007/s00032-008-0083-2

G. Lusztig, Total positivity in reductive groups, Lie theory and geometry, Progress in Mathematics, pp.531-568, 1994.
DOI : 10.1007/978-1-4612-0261-5_20

G. Lusztig, Total positivity in partial flag manifolds, p.7078, 1998.

O. Perron, Zur Theorie der Matrices, Mathematische Annalen, vol.64, issue.2, pp.248-263, 1907.
DOI : 10.1007/BF01449896

A. Pinkus, Totally positive matrices, Cambridge Tracts in Mathematics, 181, 2010.

I. J. Schoenberg and . Uber-variationsvermindernde-lineare-transformationen, ???ber variationsvermindernde lineare Transformationen, Mathematische Zeitschrift, vol.32, issue.1, pp.321-322, 1930.
DOI : 10.1007/BF01194637

K. Talaska, Combinatorial formulas for -coordinates in a totally nonnegative Grassmannian, Journal of Combinatorial Theory, Series A, vol.118, issue.1, pp.58-66, 2011.
DOI : 10.1016/j.jcta.2009.10.006
URL : https://hal.archives-ouvertes.fr/hal-01185398

G. N. Watson, A treatise on the theory of Bessel functions (2nd, 1966.