ABSTRACT
This is an alternative way to ascribe Sturm’s index to basic patterns {Fl}. Modifying the nonlinearity in the approximation (158), we consider the following operator family (watch the last term): for ε ∈ [0, 1],
Aˆε(F ) = (−1)m+1F (2m) + (1− ε) ( F − ∣∣ε2 + F 2∣∣− n2(n+1) |F |εF ). (164)
As usual, by the actual homotopic connection, we mean the corresponding vector fields composed of compact integral operators. Then, from (164) at ε = 1, we obtain the linear operator
Aˆ1(F ) = (−1)m+1F (2m).
