# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Real orthogonalizing weights for Bessel polynomials. (English) Zbl 0792.33009
The authors continue work on the real orthogonalizing weight for the generalized Bessel polynomials, see {\it K. H. Kwon}, {\it S. S. Kim} and {\it S. S. Han} [Orthogonalizing weights of Tchebychev sets of polynomials [Bull. Lond. Math. Soc. 24, No. 4, 361-367 (1992; Zbl 0768.33007)]. Using `polynomial killers’ $g$ (i.e. a distribution $g$ having moments $\langle g,x\sp n \rangle=0)$ already given by Stieltjes, their result is in the form $d \mu\sb \alpha (x)=w\sb \alpha (x)dx$ with $$w\sb \alpha (x)=x\sp \alpha \exp \left( {-2 \over x} \right) \int\sb x\sp \infty t\sp{-\alpha-2} g(t) \exp \left( {2 \over t} \right) dt\ (x>0),$$ and zero for $x \le 0$, under the condition $\int\sb 0\sp \infty w\sb \alpha (x)dx \ne 0$; this condition is satisfied for at least the choices $\alpha=0,\pm 1$.

##### MSC:
 33C45 Orthogonal polynomials and functions of hypergeometric type
Full Text:
##### References:
 [1] Boas, R. P.: The Stieltjes moment problem for functions of bounded variation. Bull. amer. Math. soc. 45, 339-404 (1949) · Zbl 0021.30702 [2] Duran, A. J.: The Stieltjes moment problem for rapidly decreasing functions. Proc. amer. Math. soc. 107, No. 3, 731-741 (1989) · Zbl 0676.44007 [3] Duran, A. J.: Functions with given moments and weight functions for orthogonal polynomials. Rocky mountain J. Math. 23, No. 1, 87-104 (1993) · Zbl 0777.44003 [4] Favard, J.: Sur LES polynômes de tchebicheff. CR acad. Sci. Paris 200, 2052-2053 (1935) · Zbl 0012.06205 [5] Grosswald, E.: Bessel polynomials. 698 (1973) · Zbl 0416.33008 [6] Kaneko, A.: Introduction to hyperfunctions. (1980) [7] Kim, S. S.; Kwon, K. H.: Hyperfunctional weights for orthogonal polynomials. Results in math. 18, 273-281 (1990) · Zbl 0734.33006 [8] Komatsu, H.: An introduction to the theory of hyperfunctions. Lecture notes in math. 287, 3-40 (1973) [9] Krall, A. M.: Orthogonal polynomials through moment generating functions. SIAM J. Math. anal. 9, 600-603 (1978) · Zbl 0389.33010 [10] Krall, A. M.: Chebyshev sets of polynomials which satisfy an ordinary differential equation. SIAM rev. 22, 436-441 (1980) · Zbl 0448.33018 [11] Krall, A. M.: The Bessel polynomial moment problem. Acta math. Acad. sci. Hungar. 38, 105-107 (1981) · Zbl 0431.33004 [12] Krall, H. L.; Frink, O.: A new class of orthogonal polynomials: the Bessel polynomials. Trans. amer. Math. soc. 65, 100-115 (1949) · Zbl 0031.29701 [13] Kwon, K. H.; Kim, S. S.; Han, S. S.: Orthogonalizing weights of tchebychev sets of polynomials. Bull. London math. Soc. 24, 361-367 (1992) · Zbl 0768.33007 [14] Littlejohn, L. L.: On the classification of differential equations having orthogonal polynomial solutions. Ann. mat. Pura appl. 4, 35-53 (1984) · Zbl 0571.34003 [15] Morton, R. D.; Krall, A. M.: Distributional weight functions for orthogonal polynomials. SIAM J. Math. anal. 9, No. 4, 604-626 (1978) · Zbl 0389.33009