共查询到20条相似文献,搜索用时 46 毫秒
1.
Luis O. Silva Julio H. Toloza 《Journal of Mathematical Analysis and Applications》2007,328(2):1087-1107
We establish sufficient conditions for self-adjointness on a class of unbounded Jacobi operators defined by matrices with main diagonal sequence of very slow growth and rapidly growing off-diagonal entries. With some additional assumptions, we also prove that these operators have only discrete spectrum. 相似文献
2.
Let be an orthonormal Jacobi polynomial of degree k. We will establish the following inequality:where δ-1<δ1 are appropriate approximations to the extreme zeros of . As a corollary we confirm, even in a stronger form, T. Erdélyi, A.P. Magnus and P. Nevai conjecture [T. Erdélyi, A.P. Magnus, P. Nevai, Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994) 602–614] by proving thatin the region . 相似文献
3.
In this paper, we give a new definition for the space of non-holomorphic Jacobi Maaß forms (denoted by J k,m nh ) of weight k∈? and index m∈? as eigenfunctions of a degree three differential operator \(\mathcal{C}^{k,m}\). We show that the three main examples of Jacobi forms known in the literature: holomorphic, skew-holomorphic and real-analytic Eisenstein series, are contained in J k,m nh . We construct new examples of cuspidal Jacobi Maaß forms F f of weight k∈2? and index 1 from weight k?1/2 Maaß forms f with respect to Γ0(4) and show that the map f ? F f is Hecke equivariant. We also show that the above map is compatible with the well-known representation theory of the Jacobi group. In addition, we show that all of J k,m nh can be “essentially” obtained from scalar or vector valued half integer weight Maaß forms. 相似文献
4.
5.
We study the translation and the convolution associated to the discrete Jacobi transformation on complex sequences of slow
and rapid growth. Also we establish new topological properties for these spaces of sequences.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
We consider a class of Jacobi matrices with unbounded coefficients. This class is known to exhibit a first-order phase transition in the sense that, as a parameter is varied, one has purely discrete spectrum below the transition point and purely absolutely continuous spectrum above the transition point. We determine the spectral type and solution asymptotics at the transition point. 相似文献
7.
Clemens Markett 《Indagationes Mathematicae》2019,30(1):81-93
For a long time it has been a challenging goal to identify all orthogonal polynomial systems that occur as eigenfunctions of a linear differential equation. One of the widest classes of such eigenfunctions known so far, is given by Koornwinder’s generalized Jacobi polynomials with four parameters and determining the orthogonality measure on the interval . The corresponding differential equation of order is presented here as a linear combination of four elementary components which make the corresponding differential operator widely accessible for applications. In particular, we show that this operator is symmetric with respect to the underlying scalar product and thus verify the orthogonality of the eigenfunctions. 相似文献
8.
9.
Vladimir D. Stepanov 《Proceedings of the American Mathematical Society》2008,136(5):1589-1597
For a weight function generating the classical Jacobi polynomials, the sharp double estimate of the distance from the subspace of all polynomials of an arbitrary fixed order is established.
10.
We investigate the spectral properties of a class of Jacobi
matrices resulting from periodic pertubations of Jacobi operators with
smooth coefficients. 相似文献
11.
Bidyut Guha Thakurta 《Proceedings Mathematical Sciences》1986,95(1):53-59
In this paper, Weisner’s group-theoretic method of obtaining generating functions is utilized in the study of Jacobi polynomialsP> n (a,ß)(x) by giving suitable interpretations to the index (n) and the parameter (β) to find out the elements for constructing a six-dimensional Lie algebra. 相似文献
12.
T. Kawazoe 《分析论及其应用》2016,32(1):38-51
Let $({\Bbb R}_+,*,\Delta)$ be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley $g$ function and the Lusin area function for the Jacobi hypergroup and consider their $(H^1, L^1)$ boundedness. Although the $g$ operator for $({\Bbb R}_+,*,\Delta)$ possesses better property than the classical $g$ operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the $(H^1, L^1)$ estimate for the Lusin area operator, a slight modification in its form is required. 相似文献
13.
S. Kupin 《Proceedings of the American Mathematical Society》2004,132(5):1377-1383
Let be a Jacobi matrix with elements on the main diagonal and elements on the auxiliary ones. We suppose that is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of coincides with , and its discrete spectrum is a union of two sequences 2, x^-_j<-2$">, tending to . We denote sequences and by and , respectively.
The main result of the note is the following theorem.
Theorem. Let be a Jacobi matrix described above and be its spectral measure. Then if and only if
-\infty,\qquad {ii)} \sum_j(x^\pm_j\mp2)^{7/2}<\infty. \end{displaymath}">
14.
We use the classical results of Baxter and Golinskii–Ibragimov to prove a new spectral equivalence for Jacobi matrices on . In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that and lie in or for s1. 相似文献
15.
Rodica D. Costin 《Journal of Approximation Theory》2009,161(2):787-801
A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a three term recurrence relation, integral inter-relations, and weak orthogonality relations. 相似文献
16.
In this paper we explore the relationship between vector-valued modular forms and Jacobi forms and give explicit relations
over various congruence subgroups. The main result is that a Jacobi form of square-free index on the full Jacobi group is
uniquely determined by any of the associated vector components. In addition, an explicit construction is given to determine
the other vector components from this single component. In other words, we give an explicit construction of a Jacobi form
from a subset of its Fourier coefficients. This leads to results about how the transformation properties are affected by congruence
restrictions on the Fourier expansion.
2000 Mathematics Subject Classification: Primary—11F50; Secondary—11F30 相似文献
17.
Joaquí n Pé rez 《Transactions of the American Mathematical Society》1997,349(6):2371-2389
The spaces of nondegenerate properly embedded minimal surfaces in quotients of by nontrivial translations or by screw motions with nontrivial rotational part, fixed finite topology and planar type ends, are endowed with natural structures of finite dimensional real analytic manifolds. This nondegeneracy is defined in terms of Jacobi functions. Riemann's minimal examples are characterized as the only nondegenerate surfaces with genus one in their corresponding spaces. We also give natural immersions of these spaces into certain complex Euclidean spaces which turn out to be Lagrangian immersions with respect to the standard symplectic structures.
18.
Shuichi Hayashida 《Journal of Number Theory》2004,106(2):200-218
The isomorphism between Kohnen's plus space and Jacobi forms of index 1 was given by Eichler-Zagier. In this article, we generalize this isomorphism for higher degree in the case of skew-holomorphic Jacobi forms. 相似文献
19.
本文证明了由广义Jacolbi权产生的Lebesgue函数在(-1,1)中任意固定内闭区间τ上的估计为O(lnn),这个结果改进了「3」中在一般抽象权时给出的结论 相似文献
20.
讨论利用给定的三个特殊次序向量对构造不可约三对角矩阵、Jacobi矩阵和负Jacobi矩阵的反问题.在求解方法中,将已知的一些关系式等价地转化为线性方程组,利用线性方程组有解的条件,得到了所研究问题有惟一解的充要条件,并给出了数值算法和例子. 相似文献