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1.
C. E. Chidume Jinlu Li A. Udomene 《Proceedings of the American Mathematical Society》2005,133(2):473-480
Let be a real Banach space with a uniformly Gâteaux differentiable norm possessing uniform normal structure, be a nonempty closed convex and bounded subset of , be an asymptotically nonexpansive mapping with sequence . Let be fixed, be such that , , and . Define the sequence iteratively by , n= 0, 1, 2, ..._. $"> It is proved that, for each integer , there is a unique such that If, in addition, and , then converges strongly to a fixed point of .
2.
Let be an integer and let . In this note we prove that for all ; if is odd and if is even This improves a classical result of Wiener and Wintner. We also give a necessary and sufficient condition for the product to approach zero at infinity.
3.
Benito J. Gonzá lez Emilio R. Negrin 《Proceedings of the American Mathematical Society》1999,127(2):619-625
Let be a complete Riemannian manifold of dimension without boundary and with Ricci curvature bounded below by where If is a vector field such that and on for some nonnegative constants and then we show that any positive solution of the equation satisfies the estimate
on , for all In particular, for the case when this estimate is advantageous for small values of and when it recovers the celebrated Liouville theorem of Yau (Comm. Pure Appl. Math. 28 (1975), 201-228).
4.
Let generate a tight affine frame with dilation factor , where , and sampling constant (for the zeroth scale level). Then for , oversampling (or oversampling by ) means replacing the sampling constant by . The Second Oversampling Theorem asserts that oversampling of the given tight affine frame generated by preserves a tight affine frame, provided that is relatively prime to (i.e., ). In this paper, we discuss the preservation of tightness in oversampling, where (i.e., and ). We also show that tight affine frame preservation in oversampling is equivalent to the property of shift-invariance with respect to of the affine frame operator defined on the zeroth scale level.
5.
William S. Cohn 《Proceedings of the American Mathematical Society》1999,127(2):509-517
We show that a function is the derivative of a function in the Hardy space of the unit disk for if and only if where and . Here, can be chosen to be non-vanishing, , and . As an application, we characterize positive measures on the unit disk such that the operator is bounded from the tent space to , where .
6.
Marek Lassak 《Proceedings of the American Mathematical Society》2002,130(10):3075-3084
Let be an arbitrary planar convex body. We prove that contains an axially symmetric convex body of area at least . Also approximation by some specific axially symmetric bodies is considered. In particular, we can inscribe a rhombus of area at least in , and we can circumscribe a homothetic rhombus of area at most about . The homothety ratio is at most . Those factors and , as well as the ratio , cannot be improved.
7.
The distribution of sequences in residue classes 总被引:1,自引:0,他引:1
Christian Elsholtz 《Proceedings of the American Mathematical Society》2002,130(8):2247-2250
We prove that any set of integers with lies in at least many residue classes modulo most primes . (Here is a positive constant.) This generalizes a result of Erdos and Ram Murty, who proved in connection with Artin's conjecture on primitive roots that the integers below which are multiplicatively generated by the coprime integers (i.e. whose counting function is also ) lie in at least residue classes, modulo most small primes , where as .
8.
K. Tanahashi A. Uchiyama M. Uchiyama 《Proceedings of the American Mathematical Society》2003,131(8):2549-2552
We show Schwarz type inequalities and consider their converses. A continuous function is said to be semi-operator monotone on if is operator monotone on . Let be a bounded linear operator on a complex Hilbert space and be the polar decomposition of . Let and for . (1) If a non-zero function is semi-operator monotone on , then for , where . (2) If are semi-operator monotone on , then for . Also, we show converses of these inequalities, which imply that semi-operator monotonicity is necessary.
9.
John R. Akeroyd 《Proceedings of the American Mathematical Society》2002,130(11):3349-3354
Let be a finite, positive Borel measure with support in such that - the closure of the polynomials in - is irreducible and each point in is a bounded point evaluation for . We show that if 0$">and there is a nontrivial subarc of such that
then for each nontrivial closed invariant subspace for the shift on .
-\infty,\end{displaymath}">
then for each nontrivial closed invariant subspace for the shift on .
10.
Zbigniew Jelonek 《Proceedings of the American Mathematical Society》2003,131(5):1361-1367
Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.
11.
Let be invertible bounded linear operators on a Hilbert space satisfying , and let be real numbers satisfying Furuta showed that if , then . This inequality is called the grand Furuta inequality, which interpolates the Furuta inequality
and the Ando-Hiai inequality ( ).
and the Ando-Hiai inequality ( ).
In this paper, we show the grand Furuta inequality is best possible in the following sense: that is, if , then there exist invertible matrices with which do not satisfy .
12.
Takahiko Nakazi 《Proceedings of the American Mathematical Society》2003,131(4):1267-1271
and denote the Hardy spaces on the open unit disc . Let be a function in and . If is an inner function and , then is orthogonal in . W.Rudin asked if the converse is true and C. Sundberg and C. Bishop showed that the converse is not true. Therefore there exists a function such that is not an inner function and is orthogonal in . In this paper, the following is shown: is orthogonal in if and only if there exists a unique probability measure on [0,1] with supp such that for nearly all in where is the Nevanlinna counting function of . If is an inner function, then is a Dirac measure at .
13.
Manuel Gonzá lez Antonio Martí nez-Abejó n 《Proceedings of the American Mathematical Society》2002,130(11):3255-3258
We show that is a local dual of , and is a local dual of , where is a Banach space. A local dual space of a Banach space is a subspace of so that we have a local representation of in satisfying the properties of the representation of in provided by the principle of local reflexivity.
14.
Richard Delaware 《Proceedings of the American Mathematical Society》2003,131(8):2537-2542
A set is -straight if has finite Hausdorff -measure equal to its Hausdorff -content, where is continuous and non-decreasing with . Here, if satisfies the standard doubling condition, then every set of finite Hausdorff -measure in is shown to be a countable union of -straight sets. This also settles a conjecture of Foran that when , every set of finite -measure is a countable union of -straight sets.
15.
Oscar Perdomo 《Proceedings of the American Mathematical Society》2002,130(11):3379-3384
The stability operator of a compact oriented minimal hypersurface is given by , where is the norm of the second fundamental form. Let be the first eigenvalue of and define . In 1968 Simons proved that for any non-equatorial minimal hypersurface . In this paper we will show that only for Clifford hypersurfaces. For minimal surfaces in , let denote the area of and let denote the genus of . We will prove that . Moreover, if is embedded, then we will prove that . If in addition to the embeddeness condition we have that , then we will prove that .
16.
In this note we provide an example of a semi-hyponormal Hilbert space operator for which is not -hyponormal for some and all .
17.
Wieslaw Pawlucki 《Proceedings of the American Mathematical Society》2005,133(2):481-484
For each positive integer we construct a -function of one real variable, the graph of which has the following property: there exists a real function on which is -extendable to , for each finite, but it is not -extendable.
18.
J. Hagler 《Proceedings of the American Mathematical Society》2002,130(11):3313-3324
Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .
19.
Emre Alkan 《Proceedings of the American Mathematical Society》2003,131(6):1673-1680
Let be a cusp form with integer weight that is not a linear combination of forms with complex multiplication. For , let
Improving on work of Balog, Ono, and Serre we show that for almost all , where is any good function (e.g. such as ) monotonically tending to infinity with . Using a result of Fouvry and Iwaniec, if is a weight 2 cusp form for an elliptic curve without complex multiplication, then we show for all that . We also obtain conditional results depending on the Generalized Riemann Hypothesis and the Lang-Trotter Conjecture.
Improving on work of Balog, Ono, and Serre we show that for almost all , where is any good function (e.g. such as ) monotonically tending to infinity with . Using a result of Fouvry and Iwaniec, if is a weight 2 cusp form for an elliptic curve without complex multiplication, then we show for all that . We also obtain conditional results depending on the Generalized Riemann Hypothesis and the Lang-Trotter Conjecture.
20.
G. Paouris 《Proceedings of the American Mathematical Society》2005,133(2):565-575
We discuss the following question: Do there exist an absolute constant 0$"> and a sequence tending to infinity with , such that for every isotropic convex body in and every the inequality holds true? Under the additional assumption that is 1-unconditional, Bobkov and Nazarov have proved that this is true with . The question is related to the central limit properties of isotropic convex bodies. Consider the spherical average . We prove that for every and every isotropic convex body in , the statements (A) ``for every , " and (B) ``for every , , where " are equivalent.