“A Tensorial Form of the Theory of Functions”. An Engineering Application to: Polynomial Interpolation

Abstract

FROM BASICCONCEPTS SUCH AS: TEN SOR CAL CU LUS (FLÜGGE, 1972); FUNCTIONAL ANALYSIS (MIKHLIN, 1964) AND SOLID MECHANICS (SOEDEL, 1972) THE OBJECTIVE OF THIS OBJETIVE IS TO SHOW THAT BESIDES THE "N" COVARIANT FUNCTIONS (OF FUNCTIONAL ANALYSIS), LINEARLY INDEPENDENT AND NOT NECESSARILY ORTHOGONAL, THERE IS ANOTHER GROUP OF "N" CONTRAVARIANT FUNCTIONS THAT ARE BIORTHOGONAL TO THE FORMER GROUP. THE PRESENTATION OF THESE TWO FAMILIES GIVES RISE TO A NEW FORMULATION OF FUNCTIONAL ANALYSIS IN SKEW COORDINATES. WE WILL SEE THAT THE CONCEPT OF SKEW MAN I FOLDS FINDS IMMEDIATE APPLICABILITY TO THE PROBLEM OF INTERPOLATION OF ARBITRARY FUNCTIONS VIA THE USE OF THE NEW CONCEPT OF COVARIANT AND CONTRAVARIANT POLYNOMIALS. THE THEORY AND THE EXAMPLES DEMONSTRATE THAT THE PROBLEMS OF INTERPOLATION AND FOURIER ANALYSIS CAN BE GROUPED INTO ONE SINGLE THEORY.