We introduce the notion of uniformly refinable map for compact, Hausdorff spaces, as a generalization maps originallydefined metric continua by Jo Ford (Heath) and Jack W. Rogers, Jr., Refinable maps, Colloq. Math., 39 (1978), 263-269.

The classic Atiyah-Singer index theory of elliptic operators on compact manifolds has been vastly generalized to higher index theories of elliptic operators on noncompact spaces in the framework of noncommutative geometry [5] by Connes-Moscovici for covering spaces [8], Baum-Connes for spaces with proper and cocompact discrete group actions [2], Connes-Skandalis for foliated manifolds [9], and ...

In this paper, we consider the existence of multiple periodic solutions for the problem du , . , — +Lu = g(u) + h, r>0, dt "(0) = u(T), where L is a uniformly strongly elliptic operator with domain D(L) = Hjf(Q), g: R —► R is a continuous mapping, T > 0 and h: (0,T) —> HTM(Q.) is a measurable function.

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrödinger operator with electromagnetic potential.

We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, a fixed complex number $a\neq0$ function from the Selberg class $\mathcal{L}$, we prove Riemann-von Mangoldt formula of a-points $\Delta$-factor equation $\mathcal{L}$ an analog Landau's over these points. From last that ordinates $a$-points are unifor...

In [2] the notion of “uniformly ideal” was introduced and developed the basic theory. In this article we introduce and advance a theory which, in a sense, dual to that i.e, the notion of “uniformly secondary module”.