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1.
Karlheinz Grö chenig Amos Ron 《Proceedings of the American Mathematical Society》1998,126(4):1101-1107
Based on Ron and Shen's new method for constructing tight wave-let frames, we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness.
2.
We characterize weak compactness and weak conditional compactness of subsets of in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.
3.
Gerard Misiolek 《Proceedings of the American Mathematical Society》1996,124(3):977-982
An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnold.
4.
Ha Huy Khoai 《Proceedings of the American Mathematical Society》1997,125(12):3527-3532
We show a class of perturbations of the Fermat hypersurface such that any holomorphic curve from into is degenerate. Applying this result, we give explicit examples of hyperbolic surfaces in of arbitrary degree , and of curves of arbitrary degree in with hyperbolic complements.
5.
Two simple constructive methods are presented to compute compactly supported tight wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF conditions in the multivariate setting. We use one of our constructive methods in order to find tight wavelet frames associated with multivariate box splines, e.g., bivariate box splines on a three or four directional mesh. Moreover, a construction of tight wavelet frames with maximum vanishing moments is given, based on rational masks for the generators. For compactly supported bi-frame pairs, another simple constructive method is presented. 相似文献
6.
J. Garcí a-Falset A. Jimé nez-Melado E. Lloré ns-Fuster 《Proceedings of the American Mathematical Society》1997,125(9):2633-2636
We show that for any renorming of , the well known fixed point free mappings by Kakutani, Baillon and others are not nonexpansive.
7.
R. Cheng A. G. Miamee M. Pourahmadi 《Proceedings of the American Mathematical Society》1998,126(8):2333-2340
Fix a positive integer and . We provide expressions for the weighted distance
where is normalized Lebesgue measure on the unit circle, is a nonnegative integrable function, and ranges over the trigonometric polynomials with frequencies in
or
These distances are related to other extremal problems, and are shown to be positive if and only if is integrable. In some cases they are expressed in terms of the series coefficients of the outer functions associated with .
8.
For a finite measure , let denote the space of -measurable functions equipped with the topology of convergence in measure. We prove that a series in is subseries (or unconditionally) convergent provided each of its lacunary subseries converges.
9.
F. Azarpanah 《Proceedings of the American Mathematical Society》1997,125(7):2149-2154
The infinite intersection of essential ideals in any ring may not be an essential ideal, this intersection may even be zero. By the topological characterization of the socle by Karamzadeh and Rostami (Proc. Amer. Math.Soc. 93 (1985), 179-184), and the topological characterization of essential ideals in Proposition 2.1, it is easy to see that every intersection of essential ideals of is an essential ideal if and only if the set of isolated points of is dense in . Motivated by this result in , we study the essentiallity of the intersection of essential ideals for topological spaces which may have no isolated points. In particular, some important ideals and , which are the intersection of essential ideals, are studied further and their essentiallity is characterized. Finally a question raised by Karamzadeh and Rostami, namely when the socle of and the ideal of coincide, is answered.
10.
J. Wu 《Proceedings of the American Mathematical Society》1998,126(1):1-8
In this note, we prove that for every and , the short interval contains at least one prime number of the form with . This improves a similar result due to Huxley and Iwaniec, which requires .
11.
J. A. Erdos 《Proceedings of the American Mathematical Society》1996,124(4):1127-1131
Anoussis and Katsoulis have obtained a criterion for the space to have a closed complement in , where is a completely distributive commutative subspace lattice. They show that, for a given , the set of for which this complement exists forms an interval whose endpoints are harmonic conjugates. Also, they establish the existence of a lattice for which has no complement for any . However, they give no specific example. In this note an elementary demonstration of a simple example of this phenomenon is given. From this it follows that for a wide range of lattices , fails to have a complement for any .
12.
I. A. Semaev. 《Mathematics of Computation》1998,67(221):353-356
We show that to solve the discrete log problem in a subgroup of order of an elliptic curve over the finite field of characteristic one needs operations in this field.
13.
The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of or .
14.
Lihua Yang 《Proceedings of the American Mathematical Society》1999,127(2):455-464
This paper is concerned with unconditional basic sequences in . We prove that, under some conditions, a sequence in is a bounded unconditional basic sequence if and only if it is -stable. At last the results are applied to the shift-invariant basic sequences generated by a finite subset of , which is very important in wavelet analysis.
15.
Ilkka Holopainen Seppo Rickman 《Proceedings of the American Mathematical Society》1996,124(6):1783-1788
In 1929 L. V. Ahlfors proved the Denjoy conjecture which states that the order of an entire holomorphic function of the plane must be at least if the map has at least finite asymptotic values. In this paper, we prove that the Denjoy theorem has no counterpart in the classical form for quasiregular maps in dimensions . We construct a quasiregular map of with a bounded order but with infinitely many asymptotic limits. Our method also gives a new construction for a counterexample of Lindelöf's theorem for quasiregular maps of .
16.
Galia Dafni 《Proceedings of the American Mathematical Society》1998,126(10):2933-2943
We give a necessary condition for a distribution with compact support in a hypersurface to be in the local Hardy space . We apply this condition to prove a result distinguishing two types of Hardy spaces of distributions on a smooth domain .
17.
Peter Li Luen-fai Tam DaGang Yang 《Transactions of the American Mathematical Society》1998,350(3):1045-1078
We study the elliptic equation on complete noncompact Riemannian manifolds with nonnegative. Three fundamental theorems for this equation are proved in this paper. Complete analyses of this equation on the Euclidean space and the hyperbolic space are carried out when is a constant. Its application to the problem of conformal deformation of nonpositive scalar curvature will be done in the second part of this paper.
18.
Numerical solutions of semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundary elements. Because of the various combinations of Dirichlet, Neumann and Robin boundary conditions, there is an associated matrix problem, the norm of which must be estimated. From the analysis of such matrices, we formulate conditions which guarantee the monotone iteration a strict contraction staying within the close range of a given pair of subsolution and supersolution. Thereafter, boundary element error analysis can be carried out in a similar way as for the discretized problem. A concrete example of a monotone dissipative system on a 2D annular domain is also computed and illustrated.
19.
T. S. S. R. K. Rao 《Proceedings of the American Mathematical Society》1999,127(10):2969-2973
For an infinite compact set and for any Banach space we show that the unit ball of the space of -valued functions that are continuous when is equipped with the weak topology, has no denting points.
20.
Menachem Kojman Saharon Shelah 《Proceedings of the American Mathematical Society》1998,126(8):2459-2465
The existence of a Dowker space of cardinality and weight is proved in ZFC using pcf theory.