Heat kernels of the discrete Laguerre operators

Kostenko, Aleksey

doi:10.1007/s11005-021-01372-7

Cited by 4 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Till date, various proofs of Hardy inequalities exist, most recent ones being [13], [6], [20], [18], [17]. It is worthwhile to mention papers [8], [11], [14], [2], [7], [4], [23], [22], [3], [14], [15], [16], where various variants of inequality (1.1) have been studied and applied.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional discrete Hardy and Rellich inequalities on integers

Gupta¹

2021

Preprint

View full text Add to dashboard Cite

In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights of the form n α . We prove the inequality when α is an even natural number with the sharp constant and remainder terms. We also find explicit constants in standard and weighted Rellich inequalities and its higher order versions. As a by-product of this work we derive a combinatorial identity using purely analytic methods. This suggests a correlation between combinatorial identities and functional identities.

show abstract

Section: Introductionmentioning

confidence: 99%

One-dimensional discrete Hardy and Rellich inequalities on integers

Gupta¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

One-Dimensional Discrete Hardy and Rellich Inequalities on Integers

Gupta

2024

J Fourier Anal Appl

View full text Add to dashboard Cite

In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights of the form $$n^\alpha $$ n α . We prove the inequality when $$\alpha $$ α is an even natural number with the sharp constant and remainder terms. We also find explicit constants in standard and weighted Rellich inequalities(with weights $$n^\alpha $$ n α ) which are asymptotically sharp as $$\alpha \rightarrow \infty $$ α → ∞ . As a by-product of this work we derive a combinatorial identity using purely analytic methods, which suggests a plausible correlation between combinatorial and functional identities.

show abstract

Trace formulas and inverse spectral theory for generalized indefinite strings

Eckhardt,

Kostenko

2024

Invent. math.

View full text Add to dashboard Cite

Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and $2\times 2$ 2 × 2 canonical systems). We prove a number of Szegő-type theorems for generalized indefinite strings and related spectral problems (including Krein strings, canonical systems and Dirac operators). More specifically, for several classes of coefficients (that can be regarded as Hilbert–Schmidt perturbations of model problems), we provide a complete characterization of the corresponding set of spectral measures. In particular, our results also apply to the isospectral Lax operator for the conservative Camassa–Holm flow and allow us to establish existence of global weak solutions with various step-like initial conditions of low regularity via the inverse spectral transform.

show abstract

Heat kernels of the discrete Laguerre operators

Cited by 4 publications

References 27 publications

One-dimensional discrete Hardy and Rellich inequalities on integers

One-dimensional discrete Hardy and Rellich inequalities on integers

One-Dimensional Discrete Hardy and Rellich Inequalities on Integers

Trace formulas and inverse spectral theory for generalized indefinite strings

Contact Info

Product

Resources

About