() ar X iv 1 41 2 64 00 v1 [ m at h C A ] 5 D ec 2 01 4 Kolmogorov n Widths of Function Classes Induced by a Non Degenerate Differential Operator A Convex Duality Approach∗ Patrick L Combettes1 and Dinh Dũng2 1Sorbonne Universités – UPMC Univ Paris 06 UMR 7598, Laboratoire Jacques Louis Lions F 75005 Paris, France plc@ljll math upmc fr 2Information Technology Institute Vietnam National University Hanoi, Vietnam dinhzung@gmail com Abstract Let P(D) be the differential operator induced by a polyn[.]