摘要:

LetEbe a closed subset of a locally compact Abelian group Г and letk(E) be the space of absolutely convergent Fourier transforms on Г that vanish onE. (1)k(E) is characterized as an ideal of arithmetic means defined by the behavior of pseudo‐measures at infinity; and so spectral synthesis holds for an idealIifIand its corresponding ideal of arithmetic means coincide. (2) We then prove that it is possible to synthesize pseudomeasures at infinity in a manner that runs parallel to Beurling's synthesis of weighted spaces. These two results are closely related by the notion of Wiener's spect

ISSN:0022-2526    

DOI:10.1002/sapm197554291

年代:1975

数据来源: WILEY

摘要:

It is shown that for any ringRof sets there is a locally convex Hausdorff topological vector spaceM(R) and a measureχ:R→M(R) such that for any other locally convex Hausdorff topological vector spaceWand any measureµ:R→W, there exists a unique continuous linear mapµ:M(R) →Wsuch that . Measure is defined in such a way thatM(R)′, the space of all continuous linear functionals onM(R), corresponds to all finite, signed measures in the usual sense whenRis aσ‐ring. The problem of extending measures fromRto theσ‐ring generated byRis formulted in this setting. Properties of the universal measureχare described. The topology ofM(R) is studied via the pairing. For example, the weak compact subsets ofM(R)′ are characterized. This characterization gives rise to a simple proof of the

ISSN:0022-2526    

DOI:10.1002/sapm1975542117

年代:1975

数据来源: WILEY

摘要:

Let Δ be a triangulation of a (d− 1)‐dimensional sphere withnvertices. The Upper Bound Conjecture states that the number ofi‐dimensional faces of Δ is less than or equal to a certain explicit numberci(n, d). A proof is given of a more general result. The proof uses the result, proved by G. Reisner, that a certain commutative ring associated with Δ is a Cohen‐Mac

ISSN:0022-2526    

DOI:10.1002/sapm1975542135

年代:1975

数据来源: WILEY

摘要:

Pregeometries (matroids) whose independent sets are the partial matchings of a relation (transversal pregeometries) can be canonically imbedded in a free‐simplicial pregeometry (one whose points lie freely on flats spanned by a simplex). Conversely, all subgeometries of such free‐simplicial pregeometries are transversal. Free‐simplicial pregeometries are counted and their duals are naturally constructed and shown to be free‐simplicial (showing self‐dual free‐simplexes corrspond to quasisymmetric relations). For more general transversal pregeometries, modular flats are characterized and transversal contractions are exemplified. Binary transversal pregeometries and their contractions (the class of binary gammoids) are shown to be the class of series‐parallel networks, providing insight for further characterizations of (coordinatized) gammoids by excluded minors.Theorem. All principal transversal pregeometries and their truncations have critical expon

ISSN:0022-2526    

DOI:10.1002/sapm1975542143

年代:1975

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1975542161

年代:1975

数据来源: WILEY

摘要:

By solving the direct and inverse scattering problems for a rather ‘unconventional’ eigenvalue problem, we can solve the initial value problem for the sine‐Gordon equation entirely in laboratory coordinates. This allows us to extend and accurately define the class of initial value problems which can be solved by ‘inverse scattering transforms.’ Simple examples are given to illustrate both the direct and the inverse scatterin

ISSN:0022-2526    

DOI:10.1002/sapm1975542165

年代:1975

数据来源: WILEY