Anneliese Spaeth
Dr. Spaeth earned a Ph.D. in Mathematics in the area of Banach Spaces and Basis Theory at Vanderbilt University in 2013, a Master’s degree focused on Sigma Delta Quantization Theory at Vanderbilt University in 2009, and the degree of Bachelor of Science as an Honors Program University Scholar in Mathematics and Applied Physics from Xavier University, Summa Cum Laude, in 2007. Dr. Spaeth Joined the Faculty of Huntingdon College in 2012 and served as Chair of the Department of Mathematics from 2014 to 2019, during which she led the adoption of the Applied Mathematics Major. Over her years at Huntingdon, Dr. Spaeth took on various roles, including Instructional Technology Specialist and Director of Academic Technology Services and Project Management. In 2019, Dr. Spaeth assumed her present role of Associate Vice President for Technology, with the goal of developing a strategic plan to improve Huntingdon College in the area of technology. Dr. Spaeth was promoted to Vice President for Technology in June 2020.
Aside from her administrative duties, Dr. Spaeth serves on the Editorial board of the Journal of Inquiry Based Learning in Mathematics, and maintains research interests in a variety of areas, including Inquiry-Based Learning in Mathematics, RUME (Research in Undergraduate Mathematics Education), Basis Theory, Pure and Applied Harmonic Analysis, and Quantization Algorithms. Dr. Spaeth’s other academic interests include programming (particularly in Python) and technology in general. Dr. Spaeth also enjoys volunteering for the BEST Robotics program.
Supervisors: Alexander M. Powell
Aside from her administrative duties, Dr. Spaeth serves on the Editorial board of the Journal of Inquiry Based Learning in Mathematics, and maintains research interests in a variety of areas, including Inquiry-Based Learning in Mathematics, RUME (Research in Undergraduate Mathematics Education), Basis Theory, Pure and Applied Harmonic Analysis, and Quantization Algorithms. Dr. Spaeth’s other academic interests include programming (particularly in Python) and technology in general. Dr. Spaeth also enjoys volunteering for the BEST Robotics program.
Supervisors: Alexander M. Powell
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For example, we prove that if each element of the system $\{f_n\}_{n=1}^\infty \subset L^p(\R)$ is pointwise nonnegative, then
$\{f_n\}_{n=1}^{\infty}$ cannot be an unconditional basis or unconditional quasibasis (unconditional Schauder frame) for $L^p(\R)$. In particular, in $L^2(\R)$ this precludes the existence of nonnegative Riesz bases
and frames.
On the other hand, there exist pointwise nonnegative conditional quasibases in $L^p(\R)$, and there also exist pointwise nonnegative exact systems and
Markushevich bases in $L^p(\R)$.
For example, we prove that if each element of the system $\{f_n\}_{n=1}^\infty \subset L^p(\R)$ is pointwise nonnegative, then
$\{f_n\}_{n=1}^{\infty}$ cannot be an unconditional basis or unconditional quasibasis (unconditional Schauder frame) for $L^p(\R)$. In particular, in $L^2(\R)$ this precludes the existence of nonnegative Riesz bases
and frames.
On the other hand, there exist pointwise nonnegative conditional quasibases in $L^p(\R)$, and there also exist pointwise nonnegative exact systems and
Markushevich bases in $L^p(\R)$.