共查询到20条相似文献,搜索用时 15 毫秒
1.
Athanassios Tzouvaras 《Mathematical Logic Quarterly》1993,39(1):454-460
We show that there are universes of sets which contain descending ?-sequences of length α for every ordinal α, though they do not contain any ?-cycle. It is also shown that there is no set universe containing a descending ?-sequence of length On. MSC: 03E30; 03E65. 相似文献
2.
We introduce a new wide class of p-adic pseudodifferential operators. We show that the basis of p-adic wavelets is the basis of eigenvectors for the introduced operators. 相似文献
3.
S. Albeverio A. Yu. Khrennikov V.M. Shelkovich 《Journal of Fourier Analysis and Applications》2006,12(4):393-425
In this article the p-adic Lizorkin spaces of test functions and distributions are introduced. Multi-dimensional Vladimirov’s
and Taibleson’s fractional operators, and a class of p-adic pseudo-differential operators are studied on these spaces. Since
the p-adic Lizorkin spaces are invariant under these operators, they can play a key role in considerations related to fractional
operator problems. Solutions of pseudo-differential equations are also constructed. Some problems of spectral analysis of
pseudo-differential operators are studied. p-Adic multidimensional Tauberian theorems connected with these pseudo-differential
operators for the Lizorkin distributions are proved. 相似文献
4.
S. V. Kozyrev A. Yu. Khrennikov V. M. Shelkovich 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):157-196
The theory of p-adic wavelets is presented. One-dimensional and multidimensional wavelet bases and their relation to the spectral theory of pseudodifferential operators are discussed. For the first time, bases of compactly supported eigenvectors for p-adic pseudodifferential operators were considered by V.S. Vladimirov. In contrast to real wavelets, p-adic wavelets are related to the group representation theory; namely, the frames of p-adic wavelets are the orbits of p-adic transformation groups (systems of coherent states). A p-adic multiresolution analysis is considered and is shown to be a particular case of the construction of a p-adic wavelet frame as an orbit of the action of the affine group. 相似文献
5.
Mutsuro Somekawa 《K-Theory》1999,17(3):265-294
The purpose of this paper is to show that under the syntomic regulator map from the motivic cohomology to the syntomic cohomology of the integer ring of a cyclotomic field, the image of Beilinson's element is a special value of the p-adic polylogarithm. 相似文献
6.
We consider the squaring map over the p-adic numbers for an odd prime p, and study its symbolic dynamics on the unit circle in ? p , the p-adic integers. When the map is restricted to the set of squares, we show an equivalence to angle doubling (mod 1) for rational angles. For primes p ≡ 3 (mod 4), this map may be represented as a unitary permutation matrix of the type used in quantum phase estimation. 相似文献
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9.
S. Albeverio S. Evdokimov M. Skopina 《Journal of Fourier Analysis and Applications》2010,16(5):693-714
We study p-adic multiresolution analyses (MRAs). A complete characterization of test functions generating an MRA (scaling functions)
is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling
functions generate the Haar MRA. We also suggest a method for constructing sets of wavelet functions and prove that any set
of wavelet functions generates a p-adic wavelet frame. 相似文献
10.
Robert L. Benedetto 《Compositio Mathematica》2000,122(3):281-298
In this paper we study dynamics on the Fatou set of a rational function
. Using a notion of components of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points. 相似文献
11.
E. I. Zelenov 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):132-144
A p-adic realization of the standard statistical model of quantum mechanics is constructed. Within this realization, a p-adic linear bosonic channel is defined, and its properties are analyzed. In particular, a criterion for the existence of a linear Gaussian bosonic channel is obtained, and its explicit construction is described. It is shown that the p-adic Gaussian bosonic channels possess an additivity property. 相似文献
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13.
Martin Ziegler 《Applied mathematics and computation》2009,215(4):1431-1447
We turn the physical Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s):Examining recent controversies and causes for misunderstanding concerning the state of the Church-Turing Hypothesis (CTH), it is suggested to study the CTH ‘sharpened’ relative to an arbitrary but specific physical theory - rather than vaguely referring to “nature” in general. For this purpose we apply, and emphasize the utility of, concepts from philosophy: physical structuralism, ontological commitment, and constructivism. This general approach is then illustrated with some exemplary results on computability and complexity theory in computational physics. 相似文献
14.
O. F. Casas-Sánchez W. A. Zúñiga-Galindo 《P-Adic Numbers, Ultrametric Analysis, and Applications》2014,6(1):1-20
In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four dimensional vector space over the field of p-adic numbers. 相似文献
15.
引入了几类p-中心函数空间,包括p进A~q和B~q空间、p进λ-中心BMO空间以及p-进中心Morrey空间,得到了p-进A~q空间与B~q空间的对偶性、p-进λ-中心BMO空间和中心Morrey空间的特征,研究了这些空间与加权p-进Lebesgue空间之间的关系.另外,还建立了一类奇异积分算子在p-进中心Morrey空间中的有界性,更进一步,得到了这类算子交换子在p-进中心Morrey空间中的λ-中心BMO估计. 相似文献
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17.
The classical and quantum formalism for a p-adic and adelic harmonic oscillator with a time-dependent frequency is developed,
and general formulas are obtained for the main theoretical quantities. In particular, the p-adic propagator is calculated,
and the existence of a simple vacuum state as well as adelic quantum dynamics is shown. A spatial discreteness and a p-adic
quantum mechanical phase are noted.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 2, pp. 239–248, August, 2000. 相似文献
18.
Joachim Mahnkopf 《Compositio Mathematica》2000,124(3):253-304
Let be a cuspidal automorphic representation of GL3(
), unramified at pand of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions on
p
*
having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |(U)|
p
|Haar(U)|
p
for open subsets U
p
*, where Haardenotes the invariant distribution on
p
*. 相似文献
19.