commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...

Well known results related to the compactness of Hankel operators of one complex variable are extended to little Hankel operators of two complex variables. Critical to these considerations is the result of Ferguson and Lacey [5] characterizing the boundedness of the little Hankel operators in terms of the product BMO of S.-Y. Chang and R. Fefferman [2,3].

The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the Binomial or Invert transform of S. If H is the Hankel matrix of a sequence and H=LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the Binomial or Invert transform is also ...

Cauchy coeecient integrals and Hankel contours provide a natural generalization of Stirling numbers for unrestricted complex values of their arguments. Many classical identities survive such an extension. Sur les nombres de Stirling d'indice complexe et les contours de Hankel R esum e : Les int egrales de Cauchy et les contours de Hankel fournissent une g en eralisation naturelle des nombres de...