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where ui9 vtGL [0, l]9n fixed. The solution of the L 2 version of this problem is a classical result of E. Schmidt [3] (see also Courant and Hubert [1, p. 161]). For the class of strictly totally positive kernels K9 we are able to show that a best choice of functions ux, . . . , un9 vx, . . . , vn is determined by certain sections K(x, %x)9 . . . , K(x, £„), K(TV y), . . . , K(rn, y) of the kernel K. DEFINITION. A real-valued kernel K(x, y), defined and continuous on [0, 1] x [0, 1], is called strictly totally positive (S.T.P.) if all its Fredholm minors l » * • * » m \ UdetWK(sif tt)l^x 1' * • • > m)

Best mean approximation to a 2-dimensional kernel by tensor products