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By Zlatko Jankocic

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Extra info for A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969

Sample text

VI - Remarks one-to-one correspondence (6. 6) between the spaces and X (oa) X (C) would find its deeper sense in the light of the well- known theorem space f-1 sp&ce H [ 4] : Any complex (real) separable Hilbert is isometric and isomorphic to the complex (real) and, consequently, all complex (real) separable spaces are isometric and isomorphic one to another. We arenot going here to dis- cuss many possible applications of the described approach for the infinite dimensional case, but we only mention that this approach could be useful in many fields, e.

12) (X) a. I. L (x) • R Thus, the relation (6. 10a) or (6. 1"2) represents the series expansion of the function a (X) by means of the orthonormal complete set of functions (6. 11 ), the totality of the function a< values being symbolized by The natural requirement of the finite vector norm (3. ; t a. e. x

3a) ' B of the same type. 2) The difference of the field quantity A (Q) and of A ( P )Q should be a quantity of the same type of the first order in the parameter differentials A CP)Q. = A (Q) - ß AW) ~ dxk V~< ACQ) • ACQ) (1. 3b) ß A (Q) We call the quantity tial and the quantity Vk A CQ) ative of the quantity A (Q) • the the absolute differen- k - th absolute deriv- Vector and Tensor Analysis I 12 3) The absolute differentials of the basis vectors are assumed to have these explicit forms : /).

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