| Full text | |
| Author(s): |
Dimitrov, Dimitar K.
;
Gadjev, Ivan
;
Nikolov, Geno
;
Uluchev, Rumen
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 149, n. 6, p. 15-pg., 2021-06-01. |
| Abstract | |
We study the behaviour of the smallest possible constants d(n), and c(n), in Hardy's inequalities Sigma(n)(k=1) (1/k Sigma(k)(j=1) a(j))(2) <= d(n) Sigma(n)(k=1) a(k)(2), (a(1), ..., a(n)) is an element of R-n and integral(infinity)(0) (1/x integral(x)(0) f(t) dt)(2) dx <= c(n) integral(infinity)(0) f(2)(x) dx, f is an element of H-n, for the finite dimensional spaces R-n and H-n := { f : f(o)(x) f(t)dt = e(-x/2) p(x) : p is an element of P-n,p(0) = 0}, where P-n is the set of real-valued algebraic polynomials of degree not exceeding n. The constants d(n) and c(n) are identified to be expressed in terms of the smallest zeros of the so-called continuous dual Hahn polynomials and the two-sided estimates for d(n) and c(n) of the form 4 - c/In n < d(n), c(n) < 4 - c/In-2 n, c > 0 are established. (AU) | |
| FAPESP's process: | 16/10357-1 - Zeros of orthogonal polynomials and special functions and inequalities of Markov type |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |