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1.
In the present paper, we consider the classical Widder transform, the Hν-transform, the Kν-transform, and the Yν-transform. Some identities involving these transforms and many others are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and other well-known integral transforms.  相似文献   

2.
Let z α and t ν,α denote the upper 100α% points of a standard normal and a Student’s t ν distributions respectively. It is well-known that for every fixed $0<\alpha <\frac{1}{2}$ and degree of freedom ν, one has t ν,α ?>?z α and that t ν,α monotonically decreases to z α as ν increases. Recently, Mukhopadhyay (Methodol Comput Appl Probab, 2009) found a new and explicit expression b ν (?>?1) such that t ν,α ?>?b ν z α for every fixed $0<\alpha <\frac{1}{2}$ and ν. He also showed that b ν converges to 1 as ν increases. In this short note, we prove three key results: (i) $\log(b_{\nu+1}/b_{\nu})\sim -\frac{1}{4}\nu^{-2}$ for large enough ν, (ii) b ν strictly decreases as ν increases, and (iii) $b_{\nu}\sim 1+\frac14\nu^{-1}+\frac1{32}\nu^{-2}$ for large enough ν.  相似文献   

3.
It is known that the Struve function H ν and the modified Struve function L ν are closely connected to the Bessel function of the first kind J ν and to the modified Bessel function of the first kind I ν and possess representations through higher transcendental functions like the generalized hypergeometric 1 F 2 and the Meijer G function. Also, the NIST project and Wolfram formula collection contain a set of Kapteyn type series expansions for L ν (x). In this paper firstly, we obtain various another type integral representation formulae for L ν (x) using the technique developed by D. Jankov and the authors. Secondly, we present some summation results for different kind of Neumann, Kapteyn and Schlömilch series built by I ν (x) and L ν (x) which are connected by a Sonin–Gubler formula, and by the associated modified Struve differential equation. Finally, solving a Fredholm type convolutional integral equation of the first kind, Bromwich–Wagner line integral expressions are derived for the Bessel function of first kind J ν and for an associated generalized Schlömilch series.  相似文献   

4.
We completely characterize the boundedness and compactness of composition operators from the space of Cauchy transforms on the unit disk D, into the Bloch-type space Bν as well as the little Bloch-type space Bν,0, consisting respectively of all holomorphic functions f on D such that supzDν(z)|f(z)|<, that is, of all holomorphic functions f on D such that lim|z|→1ν(z)|f(z)|=0, for some weight function ν. As a byproduct of our results, norm of the operator is calculated when Bν is replaced by Bν/C.  相似文献   

5.
Let jνk, yνk and cνk denote the kth positive zeros of the Bessel functions Jν(x), Yν(x) and of the general cylinder function Cν(x), respectively. We show, among other things, that, for k = 2, 3,… and 0 < ν < ∞, cνk is a concave function of ν, cνk > ν + c0k and cνk[v + (2π)c0k] decreases as ν increases. In the cases of jνk and yνk, these results hold also for k = 1.  相似文献   

6.
A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ λ. In 1995, Griggs and Rosa posed a problem: For which values of λ 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6).  相似文献   

7.
We show that a Banach lattice X is r-convex, 1<r<∞, if and only if all positive operators T on X with values in some r-concave Köthe function spaces F(ν) (over measure spaces (Ω,ν)) factorize strongly through Lr(ν) (i.e., T=MgR, where R is an operator from X to Lr(ν) and Mg a multiplication operator on Lr(ν) with values in F). This characterization of r-convexity motivates a Maurey-Rosenthal type factorization theory for positive operators acting between vector valued Köthe function spaces.  相似文献   

8.
Let (W,H,μ) be an abstract Wiener space, and assume that νi, i=1,2, are two probability measures on (W,B(W)) which are absolutely continuous with respect to μ. Assume that the Wasserstein distance between ν1 and ν2 is finite. Then there exists a map T=IW+ξ of W into itself such that ξ:WH is measurable and 1-cyclically monotone such that the image of ν1 under T is ν2. Moreover T is invertible on the support of ν2. We give also some applications of this result such as the existence of the solutions of the Monge–Ampère equation in infinite dimensions. To cite this article: D. Feyel, A.S. Üstünel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1025–1028.  相似文献   

9.
We study a full Maxwell's system accompanied with a non-linear degenerate boundary condition, which represents a generalization of the classical Silver-Müller condition for a non-perfect conductor. The relationship between the normal components of electric E and magnetic H field obeys the following power law ν×H=ν×(|E×ν|α−1E×ν) for some α∈(0,1]. We establish the existence and uniqueness of a weak solution in a suitable function spaces under the minimal regularity assumptions on the boundary Γ and the initial data E0 and H0. We design a non-linear time discrete approximation scheme and prove convergence of the approximations to a weak solution. We also derive the error estimates for the time discretization. As a next step we study the fully discrete problem using curl-conforming edge elements and derive the corresponding error estimates. Finally we present some numerical experiments.  相似文献   

10.
LetH ν =S/S ν , whereS is the group of all permutations of a set of cardinality ? ν andS v is its subgroup of permutations moving less than ? ν elements. The infinite simple groupsH ν ,ν>0, have covering number two; that is,C 2=H ν holds for each nonunit conjugacy classC[M]. Janko’s small groupJ 1, the only finite simple group with covering number two, satisfies also: 1 $$C_{^1 } \subseteq C_{^2 } \cdot C_{^3 } for any nonunit classes C_{^1 } ,C_{^2 } ,C_{^3 } $$ . In fact,H ν (ν>0) are the only groups of covering number two where (*) is known to fail. In this paper we determine arbitrary products of classes inH ν (ν>0).  相似文献   

11.
Letμ be any probability measure on ? with ∫|x|(x)<∞ and letμ* denote the associated Hardy and Littlewood maximal p.m., the p.m. of the Hardy and Littlewood maximal function obtained fromμ. Dubins and Gilat [6] showed thatμ* is the least upper bound, in the usual stochastic order, of the collection of p.m.’sν on ? for which there is a martingale (X t )0≤t≤1 having distributions ofX 1 and sup0≤t≤1 X t given byμ andν respectively. In this paper, a type of ‘dual representation’ is given. Specifically, letν be any p.m. on ? with lim sup x →∞x ν[x,∞)=0[x, ∞)=0 and finitex 0=inf{z :ν(?∞,z]0}. Then there is a ‘minimal p.m.’ν Δ which is the greatest lower bound, in the usual convex order, of the collection of p.m.’sμ on ? for which there is a martingale (X t )0≤t≤1 having distributions ofX 1 and sup0≤t≤1 X t given byμ andν respectively. To demonstrate existence and to obtain identification of these minimal p.m.’s, we use, in particular, a lattice structure on the set of p.m.’s with the convex order, and an equivalence between a convex order of p.m.’s and the stochastic order of their maximal p.m.’s. Consequences of these order results include sharp expectation-based inequalities for martingales. These martingale inequalities form a new class of ‘prophet inequalities’ in the context of optimal stopping theory.  相似文献   

12.
We obtain upper bounds on the number of solutions to congruences of the type (x 1 + s)... (x ν + s) ≡ (y 1 + s)... (x ν + s) ? 0 (mod p) modulo a prime p with variables from some short intervals. We give some applications of our results and in particular improve several recent estimates of J. Cilleruelo and M.Z. Garaev on exponential congruences and on cardinalities of products of short intervals, some double character sum estimates of J. Friedlander and H. Iwaniec and some results of M.-C. Chang and A.A. Karatsuba on character sums twisted with the divisor function.  相似文献   

13.
For integers n≥4 and νn+1, let ex(ν;{C3,…,Cn}) denote the maximum number of edges in a graph of order ν and girth at least n+1. The {C3,…,Cn}-free graphs with order ν and size ex(ν;{C3,…,Cn}) are called extremal graphs and denoted by EX(ν;{C3,…,Cn}). We prove that given an integer k≥0, for each n≥2log2(k+2) there exist extremal graphs with ν vertices, ν+k edges and minimum degree 1 or 2. Considering this idea we construct four infinite families of extremal graphs. We also see that minimal (r;g)-cages are the exclusive elements in EX(ν0(r,g);{C3,…,Cg−1}).  相似文献   

14.
We show that every K 4-free planar graph with at most ν edge-disjoint triangles contains a set of at most ${\frac32\nu}$ edges whose removal makes the graph triangle-free. Moreover, equality is attained only when G is the edge-disjoint union of 5-wheels plus possibly some edges that are not in triangles. We also show that the same statement is true if instead of planar graphs we consider the class of graphs in which each edge belongs to at most two triangles. In contrast, it is known that for any c?<?2 there are K 4-free graphs with at most ν edge-disjoint triangles that need more than edges to cover all triangles.  相似文献   

15.
In the space L 2(T ν ×T ν ), where T ν is a ν-dimensional torus, we study the spectral properties of the “three-particle” discrete Schrödinger operator ? = H0 + H1 + H2, where H0 is the operator of multiplication by a function and H1 and H2 are partial integral operators. We prove several theorems concerning the essential spectrum of ?. We study the discrete and essential spectra of the Hamiltonians Ht and h arising in the Hubbard model on the three-dimensional lattice.  相似文献   

16.
Symmetric (ν, κ, λ)-block designs admitting polarity maps are shown to be closely related to certain Ramsey numbers for bipartite graphs. In particular, if there exists a (ν, κ, λ)-difference set in an abelian group of order ν, then the Ramsey number R(K2,λ+1, K1,ν?k+1) is either 1 + ν or 2 + ν.  相似文献   

17.
For ν≥0 let cνk be the k-th positive zero of the cylinder functionC v(t)=J v(t)cosα-Y v(t)sinα, 0≤α>π whereJ ν(t) andY ν(t) denote the Bessel functions of the first and the second kind, respectively. We prove thatC v,k 1+H(x) is convex as a function of ν, ifc νk≥x>0 and ν≥0, whereH(x) is specified in Theorem 1.1.  相似文献   

18.
19.
《Indagationes Mathematicae》2005,16(3-4):461-486
Following ideas of van Dijk and Hille we study the link which exists between maximal degenerate representations and Berezin kernels.We consider the conformal group Conf(V) of a simple real Jordan algebra V. The maximal degenerate representations πs (s ε ℂ) we shall study are induced by a character of a maximal parabolic subgroup of Conf(V). These representations πs can be realized on a space Is of smooth functions on V. There is an invariant bilinear form ℬs on the space Is. The problem we consider is to diagonalize this bilinear form ℬs, with respect to the action of a symmetric subgroup G of the conformal group Conf(V). This bilinear form can be written as an integral involving the Berezin kernel Bv an invariant kernel on the Riemannian symmetric space G/K, which is a Makarevich symmetric space in the sense of Bertram. Then we can use results by van Dijk and Pevzner who computed the spherical Fourier transform of Bv. From these, one deduces that the Berezin kernel satisfies a remarkable Bernstein identity: D(ν)Bν=b(ν)Bν+1, where D(ν) is an invariant differential operator on G/K and b(ν) is a polynomial. By using this identity we compute a Hua type integral which gives the normalizing factor for an intertwining operator from I−s to Is. Furthermore, we obtain the diagonalization of the invariant bilinear form with respect to the action of the maximal compact group U of the conformal group Conf(V).  相似文献   

20.
Let A be an n×n nonnegative matrix with the spectrum (λ1,λ2,…,λn) and let A1 be an m×m principal submatrix of A with the spectrum (μ1,μ2,…,μm). In this paper we present some cases where the realizability of (μ1,μ2,…,μm,ν1,ν2,…,νs) implies the realizability of (λ1,λ2,…,λn,ν1,ν2,…,νs) and consider the question whether this holds in general. In particular, we show that the list
(λ1,λ2,…,λn,-μ1,-μ2,…,-μm)  相似文献   

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