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Articles 181 - 184 of 184
Full-Text Articles in Mathematics
Second Leray Spectral Sequence Of Relative Hypercohomology, Saul Lubkin, Goro C. Kato
Second Leray Spectral Sequence Of Relative Hypercohomology, Saul Lubkin, Goro C. Kato
Mathematics
A second Leray spectral sequence of relative hypercohomology is constructed. (This is skew in generality to an earlier one constructed by S. Lubkin [(1968) Ann. Math. 87, 105-255].) The Mayer-Vietoris sequence of relative hypercohomology [Lubkin, S. (1968) Ann. Math. 87, 105-255] is also generalized.
Lipschitz Spaces Of Distributions On The Surface Of Unit Sphere In Euclidean N-Space, Harvey Greenwald
Lipschitz Spaces Of Distributions On The Surface Of Unit Sphere In Euclidean N-Space, Harvey Greenwald
Mathematics
In this paper Lipschitz spaces of distributions are defined and various inclusion relations are shown. Certain properties such as completeness, separability, and the density of the testing space for appropriate Lipschitz spaces are proved. The Littlewood-Paley function is defined and used to prove inclusion relationships between Lipschitz and Lebesgue spaces.
Asymptotic Numbers: Algebraic Operations With Them, Christo Ya. Christov, Todor D. Todorov
Asymptotic Numbers: Algebraic Operations With Them, Christo Ya. Christov, Todor D. Todorov
Mathematics
The main subject of the present paper is to define the four algebraic operations - additions, subtraction, multiplication and division in the set of the asymptotic numbers A [7] and to deduce the corresponding formulas for the components of the asymptotic number, representing the result as functions of the components of the arguments. The definitions of the operations, in fact, are introduced as a special case of the more general notion of a quasiclassical function - one special class of functions defined on A. The discussion of the algebraic and some other properties of the asymptotic numbers is put …
Lipschitz Spaces On The Surface Of Unit Sphere In Euclidean N-Space, Harvey Greenwald
Lipschitz Spaces On The Surface Of Unit Sphere In Euclidean N-Space, Harvey Greenwald
Mathematics
This paper is concerned with defining Lipschitz spaces on Σn-1 the surface of the unit sphere in Rn. The importance of this example is that Σn-1 is not a group but a symmetric space. One begins with functions in Lp(Σn-1),1≤p≤∞. Σn-1 is a symmetric space and is related in a natural way to the rotation group SO(n). One can then use the group SO(n) to define first and second differences for functions in Lp(Σn-1). Such a function is the boundary value of its Poisson integral. This enables one to work with functions which are harmonic. Differences can then be replaced …