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971.
We study the Besov regularity of conformal mappings for domains with rough boundary based on the well-posedness for the Dirichlet problem with Besov data. Also, sharp invertibility results for the classical layer potential operators on Sobolev-Besov spaces on the boundary of curvilinear polygons are obtained. 相似文献
972.
Using multiple q-integrals and a determinant evaluation, we establish a nonterminating 8φ7 summation for the root system Cr. We also give some important specializations explicitly. 相似文献
973.
974.
In this paper we present an inertia result for Stein equations with
an indefinite right hand side. This result is applied to establish connnections
between the inertia of invertible hermitian block Toeplitz matrices and associated
orthogonal polynomials. 相似文献
975.
976.
Manuel Barros 《Annals of Global Analysis and Geometry》1992,10(3):219-226
In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E 3? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S 3. 相似文献
977.
Summary Forf ( C
n() and 0 t x letJ
n
(f, t, x) = (–1)n
f(–x)f
(n)(t) +f(x)f
(n)
(–t). We prove that the only real-analytic functions satisfyingJ
n
(f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e
x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ
0
(f, x, x) 0 and
0
x
(x – t)n – 1Jn(f, t, x)dt 0 (n 1). 相似文献
978.
V. I. Levenshtein 《Acta Appl Math》1992,29(1-2):1-82
Finite and infinite metric spaces % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] that are polynomial with respect to a monotone substitution of variable t(d) are considered. A finite subset (code) W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] is characterized by the minimal distance d(W) between its distinct elements, by the number l(W) of distances between its distinct elements and by the maximal strength (W) of the design generated by the code W. A code W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] is called a maximum one if it has the greatest cardinality among subsets of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] with minimal distance at least d(W), and diametrical if the diameter of W is equal to the diameter of the whole space % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\]. Delsarte codes are codes W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] with (W)2l(W)–1 or (W)=2l(W)–2>0 and W is a diametrical code. It is shown that all parameters of Delsarte codes W) % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] are uniquely determined by their cardinality |W| or minimal distance d(W) and that the minimal polynomials of the Delsarte codes W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] are expansible with positive coefficients in an orthogonal system of polynomials {Q
i(t)} corresponding to % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\]. The main results of the present paper consist in a proof of maximality of all Delsarte codes provided that the system {Q
i)} satisfies some condition and of a new proof confirming in this case the validity of all the results on the upper bounds for the maximum cardinality of codes W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \]% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] with a given minimal distance, announced by the author in 1978. Moreover, it appeared that this condition is satisfied for all infinite polynomial metric spaces as well as for distance-regular graphs, decomposable in a sense defined below. It is also proved that with one exception all classical distance-regular graphs are decomposable. In addition for decomposable distance-regular graphs an improvement of the absolute Delsarte bound for diametrical codes is obtained. For the Hamming and Johnson spaces, Euclidean sphere, real and complex projective spaces, tables containing parameters of known Delsarte codes are presented. Moreover, for each of the above-mentioned infinite spaces infinite sequences (of maximum) Delsarte codes not belonging to tight designs are indicated. 相似文献
979.
Toeplitz and Hankel type operators on the upper half-plane 总被引:3,自引:0,他引:3
An orthogonal decomposition of admissible wavelets is constructed via the Laguerre polynomials, it turns to give a complete decomposition of the space of square integrable functions on the upper half-plane with the measurey
dxdy. The first subspace is just the weighted Bergman (or Dzhrbashyan) space. Three types of Ha-plitz operators are defined, they are the generalization of classical Toeplitz, small and big Hankel operators respectively. Their boundedness, compactness and Schatten-von Neumann properties are studied.Research was supported by the National Natural Science Foundation of China. 相似文献
980.
Walter Benz 《Aequationes Mathematicae》1992,43(2-3):177-182
Summary The following theorem holds true.
Theorem.
Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k. 相似文献