Injectivity sets of the Pompeiu transform

Abstract

The electronic properties of the ferrous ion in [Fe(H20),](YH,)2(S0,), are investigated using far-infrared (FIR) Fourier transform spectra and FIREPR measurements at low temperatures in the energy range from 8 to 100cm-I. Several absorption lines can be identified to originate from electronic excitations of the ferrous ion.

Infinite systems of convolution equations on multidimensional domains

“…For this reason, in relation to the results of [9] mentioned above, of interest is the following problem.…”

“…In [9], it was shown, in particular, that if n ≥ 3, then the set Φ contains all distributions ϕ ∈ Ᏸ'(‫ޓ‬ n -1 ) with infinite spectrum containing the pair (0, 1) for which suppϕ = ‫ޓ‬ n -1 (at n = 2, this is true under certain addi tional assumptions; see [9, Section 1]). Generally, the infinity condition on the spectrum cannot be relaxed; however, counterexamples are known only for nonsimply connected domains ᏻ (see [9,Lemma 23]).…”

“…Generally, the infinity condition on the spectrum cannot be relaxed; however, counterexamples are known only for nonsimply connected domains ᏻ (see [9,Lemma 23]). …”

“…In [9], a descrip tion of I(-ϕ ) for distributions ϕ ∈ Ᏸ'(‫ޓ‬ n -1 ) for which suppϕ = ‫ޓ‬ n -1 and spec ϕ is an infinite set containing (0, 1) was also obtained (at n = 2, the condition that the spectrum is infinite is replaced by a somewhat stronger requirement; see [9,Section 1]). where Λ(ᏻ, ϕ) = {ζ ∈ M(n): suppζϕ ⊂ ᏻ} and the bar denotes closure.…”

“…Some progress in this direction was made in [9], where a description of I(-) was obtained for a large class of families -consisting of distributions sup ported on the sphere. For such distributions ϕ, an important role in the question under consideration is played by the notion of spectrum in the expansion of ϕ in spherical harmonics.…”