E. Zikkos

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20222025

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4 papers · 1 filter

math.FA2025

On Markushevich bases ${x^{λ_{n}}}_{n = 1}^{\infty}$ for their closed span in weighted $L^{2} (A)$ spaces over sets $A \subset [0, \infty)$ of positive Lebesgue measure, hereditary completeness, and moment problems

Elias Zikkos

Inspired by the work of Borwein and Erdelyi \cite{BE1997JAMS} on generalizations of Müntz's theorem, we investigate the properties of the system ${x^{λ_{n}}}_{n = 1}^{\infty}$ in wei…

math.FA2025

On Strong Markushevich bases ${t^{λ_{n}}}_{n = 1}^{\infty}$ in their closed span in $L^{2} (0, 1)$ and characterizing a subspace of $H^{2} (D)$

Elias Zikkos

Let $Λ = {λ_{n}}_{n = 1}^{\infty}$ be a strictly increasing sequence of positive real numbers such that $\sum_{n = 1}^{\infty} \frac{1}{λ _{n}} < \infty$ and $in f (λ_{n + 1} - λ_{n}) > 0$ . We investig…

math.FA2024

On exact systems ${t^{α} \cdot e^{2 π in t}}_{n \in Z ∖ A}$ in $L^{2} (0, 1)$ which are not Schauder Bases and their generalizations

Elias Zikkos

Let ${e^{i λ_{n} t}}_{n \in Z}$ be an exponential Schauder Basis for $L^{2} (0, 1)$ , for $λ_{n} \in R$ , and let ${r_{n} (t)}_{n \in Z}$ be its dual Schauder Basis. Le…

math.FA2024

Hereditary completeness of Exponential systems ${e^{λ_{n} t}}_{n = 1}^{\infty}$ in their closed span in $L^{2} (a, b)$ and Spectral Synthesis

Elias Zikkos, Gajath Gunatillake

Suppose that ${λ_{n}}_{n = 1}^{\infty}$ is a sequence of distinct positive real numbers satisfying the conditions inf ${λ_{n + 1} - λ_{n}} > 0,$ and $\sum_{n = 1}^{\infty} λ_{n}^{- 1} < \infty.$ W…

On Markushevich bases {xλn​}n=1∞​ for their closed span in weighted L2(A) spaces over sets A⊂[0,∞) of positive Lebesgue measure, hereditary completeness, and moment problems

On Strong Markushevich bases {tλn​}n=1∞​ in their closed span in L2(0,1) and characterizing a subspace of H2(D)

On exact systems {tα⋅e2πint}n∈Z∖A​ in L2(0,1) which are not Schauder Bases and their generalizations

Hereditary completeness of Exponential systems {eλn​t}n=1∞​ in their closed span in L2(a,b) and Spectral Synthesis

On Markushevich bases ${x^{λ_{n}}}_{n = 1}^{\infty}$ for their closed span in weighted $L^{2} (A)$ spaces over sets $A \subset [0, \infty)$ of positive Lebesgue measure, hereditary completeness, and moment problems

On Strong Markushevich bases ${t^{λ_{n}}}_{n = 1}^{\infty}$ in their closed span in $L^{2} (0, 1)$ and characterizing a subspace of $H^{2} (D)$

On exact systems ${t^{α} \cdot e^{2 π in t}}_{n \in Z ∖ A}$ in $L^{2} (0, 1)$ which are not Schauder Bases and their generalizations

Hereditary completeness of Exponential systems ${e^{λ_{n} t}}_{n = 1}^{\infty}$ in their closed span in $L^{2} (a, b)$ and Spectral Synthesis