共查询到20条相似文献,搜索用时 15 毫秒
1.
Explicit formulas for sharp coefficients in estimates of the modulus of an analytic function and its derivative in the upper
half-plane are found. It is assumed that the boundary values of the real part of the function are in L
p
. As corollaries, sharp estimates for the modulus of the gradient of a harmonic function in
\mathbb R+2 {\mathbb R}_{+}^2 are deduced. Besides, a representation for the best constant in the estimate of the modulus of the gradient of a harmonic
function in
\mathbb R+n {\mathbb R}_{+}^n by the L
p
-norm of the boundary normal derivative is given,
1 \leqslant p \leqslant ¥ 1 \leqslant p \leqslant \infty . This representation is formulated in terms of an optimization problem on the unit sphere which is solved for p ∈ [1, n]. Bibliography: 6 titles. 相似文献
2.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
3.
Bronius Grigelionis 《Lithuanian Mathematical Journal》2011,51(2):194-206
We prove that the Thorin class $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 , is the minimal class of probability distributions on
\mathbbR+ {\mathbb{R}_{+} } that is closed under convolutions and weak limits and contains the Tweedie distributions Tw(κ+1)/κ
(μ, λ), μ > 0, λ > 0. 相似文献
4.
Mahmoud Baroun Lahcen Maniar Roland Schnaubelt 《Integral Equations and Operator Theory》2009,65(2):169-193
We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with
inhomogeneous boundary values on
\mathbbR{\mathbb{R}} and
\mathbbR±\mathbb{R}_{\pm}, if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the ‘Acquistapace–Terreni’
conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals ( − ∞, − T] and [T, ∞), then we obtain a Fredholm alternative of the equation on
\mathbbR{\mathbb{R}} in the space of functions being asymptotically almost periodic on
\mathbbR+{\mathbb{R}}_{+} and
\mathbbR-\mathbb{R}_{-}. 相似文献
5.
Clément de Seguins Pazzis 《Archiv der Mathematik》2010,95(4):333-342
When
\mathbbK{\mathbb{K}} is an arbitrary field, we study the affine automorphisms of
Mn(\mathbbK){{\rm M}_n(\mathbb{K})} that stabilize
GLn(\mathbbK){{\rm GL}_n(\mathbb{K})}. Using a theorem of Dieudonné on maximal affine subspaces of singular matrices, this is easily reduced to the known case
of linear preservers when n > 2 or # ${\mathbb{K} > 2}${\mathbb{K} > 2}. We include a short new proof of the more general Flanders theorem for affine subspaces of
Mp,q(\mathbbK){{\rm M}_{p,q}(\mathbb{K})} with bounded rank. We also find that the group of affine transformations of
M2(\mathbbF2){{\rm M}_2(\mathbb{F}_2)} that stabilize
GL2(\mathbbF2){{\rm GL}_2(\mathbb{F}_2)} does not consist solely of linear maps. Using the theory of quadratic forms over
\mathbbF2{\mathbb{F}_2}, we construct explicit isomorphisms between it, the symplectic group
Sp4(\mathbbF2){{\rm Sp}_4(\mathbb{F}_2)} and the symmetric group
\mathfrakS6{\mathfrak{S}_6}. 相似文献
6.
Sorin G. Gal 《Complex Analysis and Operator Theory》2012,6(2):515-527
Attaching to a compact disk
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} in the quaternion field
\mathbbH{\mathbb{H}} and to some analytic function in Weierstrass sense on
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} the so-called q-Bernstein operators with q ≥ 1, Voronovskaja-type results with quantitative upper estimates are proved. As applications, the exact orders of approximation
in
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} for these operators, namely
\frac1n{\frac{1}{n}} if q = 1 and
\frac1qn{\frac{1}{q^{n}}} if q > 1, are obtained. The results extend those in the case of approximation of analytic functions of a complex variable in disks
by q-Bernstein operators of complex variable in Gal (Mediterr J Math 5(3):253–272, 2008) and complete the upper estimates obtained for q-Bernstein operators of quaternionic variable in Gal (Approximation by Complex Bernstein and Convolution-Type Operators, 2009; Adv Appl Clifford Alg, doi:, 2011). 相似文献
7.
We study the limiting behavior of the K?hler–Ricci flow on
\mathbbP(O\mathbbPn ?O\mathbbPn(-1)?(m+1)){{\mathbb{P}(\mathcal{O}_{\mathbb{P}^n} \oplus \mathcal{O}_{\mathbb{P}^n}(-1)^{\oplus(m+1)})}} for m, n ≥ 1, assuming the initial metric satisfies the Calabi symmetry. We show that the flow either shrinks to a point, collapses
to
\mathbbPn{{\mathbb{P}^n}} or contracts a subvariety of codimension m + 1 in the Gromov–Hausdorff sense. We also show that the K?hler–Ricci flow resolves a certain type of cone singularities
in the Gromov–Hausdorff sense. 相似文献
8.
We determine which singular del Pezzo surfaces are equivariant compactifications of
\mathbbG\texta2 \mathbb{G}_{\text{a}}^2 , to assist with proofs of Manin’s conjecture for such surfaces. Additionally, we give an example of a singular quartic del
Pezzo surface that is an equivariant compactification of
\mathbbG\texta {\mathbb{G}_{\text{a}}} ⋊
\mathbbG\textm {\mathbb{G}_{\text{m}}} . Bibliography: 32 titles. 相似文献
9.
S. V. Hudzenko 《Ukrainian Mathematical Journal》2010,62(7):1158-1162
We consider a semigroup
FP\textfin+ ( \mathfrakS\textfin( \mathbbN ) ) FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) defined as a finitary factor power of a finitary symmetric group of countable order. It is proved that all automorphisms
of
FP\textfin+ ( \mathfrakS\textfin( \mathbbN ) ) FP_{\text{fin}}^{+} \left( {{\mathfrak{S}_{\text{fin}}}\left( \mathbb{N} \right)} \right) are induced by permutations from
\mathfrakS( \mathbbN ) \mathfrak{S}\left( \mathbb{N} \right) . 相似文献
10.
Susana D. Moura J��lio S. Neves Cornelia Schneider 《Journal of Fourier Analysis and Applications》2011,17(5):777-800
We study necessary and sufficient conditions for embeddings of Besov and Triebel-Lizorkin spaces of generalized smoothness
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), respectively, into generalized H?lder spaces
L¥,rm(·)( \mathbb Rn)\Lambda_{\infty,r}^{\mu(\cdot)}(\ensuremath {\ensuremath {\mathbb {R}}^{n}}). In particular, we are able to characterize optimal embeddings for this class of spaces provided q>1. These results improve the embedding assertions given by the continuity envelopes of
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), which were obtained recently solving an open problem of D.D. Haroske in the classical setting. 相似文献
11.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
12.
Ilham A. Aliev 《Integral Equations and Operator Theory》2009,65(2):151-167
We introduce new potential type operators Jab = (E+(-D)b/2)-a/bJ^{\alpha}_{\beta} = (E+(-\Delta)^{\beta/2})^{-\alpha/\beta}, (α > 0, β > 0), and bi-parametric scale of function spaces
Hab, p(\mathbbRn)H^{\alpha}_{\beta , p}({\mathbb{R}}^n) associated with Jαβ. These potentials generalize the classical Bessel potentials (for β = 2), and Flett potentials (for β = 1). A characterization
of the spaces
Hab, p(\mathbbRn)H^{\alpha}_{\beta, p}({\mathbb{R}}^n) is given with the aid of a special wavelet–like transform associated with a β-semigroup, which generalizes the well-known
Gauss-Weierstrass semigroup (for β = 2) and the Poisson one (for β = 1). 相似文献
13.
14.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}Let
\mathfrakg{\mathfrak{g}} be a finite dimensional simple Lie algebra over an algebraically closed field
\mathbbK\mathbb{K} of characteristic 0. Let
\mathfrakg\mathbbZ{\mathfrak{g}}_{{\mathbb{Z}}} be a Chevalley ℤ-form of
\mathfrakg{\mathfrak{g}} and
\mathfrakg\Bbbk=\mathfrakg\mathbbZ?\mathbbZ\Bbbk{\mathfrak{g}}_{\Bbbk}={\mathfrak{g}}_{{\mathbb{Z}}}\otimes _{{\mathbb{Z}}}\Bbbk, where
\Bbbk\Bbbk is the algebraic closure of
\mathbbFp{\mathbb{F}}_{p}. Let
G\BbbkG_{\Bbbk} be a simple, simply connected algebraic
\Bbbk\Bbbk-group with
\operatornameLie(G\Bbbk)=\mathfrakg\Bbbk\operatorname{Lie}(G_{\Bbbk})={\mathfrak{g}}_{\Bbbk}. In this paper, we apply recent results of Rudolf Tange on the fraction field of the centre of the universal enveloping algebra
U(\mathfrakg\Bbbk)U({\mathfrak{g}}_{\Bbbk}) to show that if the Gelfand–Kirillov conjecture (from 1966) holds for
\mathfrakg{\mathfrak{g}}, then for all p≫0 the field of rational functions
\Bbbk (\mathfrakg\Bbbk)\Bbbk ({\mathfrak{g}}_{\Bbbk}) is purely transcendental over its subfield
\Bbbk(\mathfrakg\Bbbk)G\Bbbk\Bbbk({\mathfrak{g}}_{\Bbbk})^{G_{\Bbbk}}. Very recently, it was proved by Colliot-Thélène, Kunyavskiĭ, Popov, and Reichstein that the field of rational functions
\mathbbK(\mathfrakg){\mathbb{K}}({\mathfrak{g}}) is not purely transcendental over its subfield
\mathbbK(\mathfrakg)\mathfrakg{\mathbb{K}}({\mathfrak{g}})^{\mathfrak{g}} if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4. We prove a modular version of this result (valid for p≫0) and use it to show that, in characteristic 0, the Gelfand–Kirillov conjecture fails for the simple Lie algebras of the
above types. In other words, if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4, then the Lie field of
\mathfrakg{\mathfrak{g}} is more complicated than expected. 相似文献
15.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
16.
Alexander N. Dranishnikov Yuli B. Rudyak 《Journal of Fixed Point Theory and Applications》2009,6(1):165-177
It follows from a theorem of Gromov that the stable systolic category catstsys M{\rm cat}_{\rm stsys} M of a closed manifold M is bounded from below by
cl\mathbbQ M{\rm cl}_{\mathbb{Q}} M, the rational cup-length of M [Ka07]. We study the inequality in the opposite direction. In particular, combining our results with Gromov’s theorem, we
prove the equality
catstsys M = cl\mathbbQ M{\rm cat}_{\rm stsys} M = {\rm cl}_{\mathbb{Q}} M for simply connected manifolds of dimension ≤ 7. 相似文献
17.
The main results of the paper are: (1) The boundedness of singular integral operators in the variable exponent Lebesgue spaces
L
p(·)(Γ, w) on a class of composed Carleson curves Γ where the weights w have a finite set of oscillating singularities. The proof of this result is based on the boundedness of Mellin pseudodifferential
operators on the spaces
Lp(·)(\mathbbR +,dm){L^{p(\cdot )}(\mathbb{R} _{+},d\mu)} where dμ is an invariant measure on multiplicative group ${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}. (2) Criterion of local invertibility of singular integral operators with piecewise slowly oscillating coefficients acting
on L
p(·)(Γ, w) spaces. We obtain this criterion from the corresponding criteria of local invertibility at the point 0 of Mellin pseudodifferential
operators on
\mathbbR+{\mathbb{R}_{+}} and local invertibility of singular integral operators on
\mathbbR{\mathbb{R}}. (3) Criterion of Fredholmness of singular integral operators in the variable exponent Lebesgue spaces L
p(·)(Γ, w) where Γ belongs to a class of composed Carleson curves slowly oscillating at the nodes, and the weight w has a finite set of slowly oscillating singularities. 相似文献
18.
Let
\mathbbZpm \mathbb{Z}_{p^m } be the ring of integers modulo p
m
, where p is a prime and m ⩾ 1. The general linear group GL
n
(
\mathbbZpm \mathbb{Z}_{p^m } ) acts naturally on the polynomial algebra A
n
:=
\mathbbZpm \mathbb{Z}_{p^m } [x
1, …, x
n
]. Denote by
AnGL2 (\mathbbZpm ) A_n^{GL_2 (\mathbb{Z}_{p^m } )} the corresponding ring of invariants. The purpose of the present paper is to calculate this invariant ring. Our results also
generalize the classical Dickson’s theorem. 相似文献
19.
V. M. Prokip 《Ukrainian Mathematical Journal》2012,63(8):1314-1320
Polynomial n × n matrices A(x) and B(x) over a field
\mathbbF \mathbb{F} are called semiscalar equivalent if there exist a nonsingular n × n matrix P over
\mathbbF \mathbb{F} and an invertible n × n matrix Q(x) over
\mathbbF \mathbb{F} [x] such that A(x) = PB(x)Q(x). We give a canonical form with respect to semiscalar equivalence for a matrix pencil A(x) = A
0x
- A
1, where A
0 and A
1 are n × n matrices over
\mathbbF \mathbb{F} , and A
0 is nonsingular. 相似文献
20.
Yong-Kum Cho Sunggeum Hong Joonil Kim Chan Woo Yang 《Integral Equations and Operator Theory》2009,65(4):485-528
Given
W ì \mathbbZ+3\Omega \subset {\mathbb{Z}}_{+}^{3}, we discuss a necessary and sufficient condition that the triple Hilbert transform associated with any polynomial of the
form ($t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m$t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m) is bounded in
Lp(\mathbbR4)L^p({\mathbb{R}}^4). 相似文献