Avancerad sökning
Visar resultat 1 - 5 av 7 avhandlingar som matchar ovanstående sökkriterier.
1. Vector-valued Eisenstein series of congruence types and their products
Sammanfattning : Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. LÄS MER
2. Effective Distribution Theory
Sammanfattning : In this thesis we introduce and study a notion of effectivity (or computability) for test functions and for distributions. This is done using the theory of effective (Scott-Ershov) domains and effective domain representations. LÄS MER
3. Reordering in Noncommutative Algebras, Orthogonal Polynomials and Operators
Sammanfattning : The main object studied in this thesis is the multi-parametric family of unital associative complex algebras generated by the element $Q$ and the finite or infinite set $\{S_j\}_{j\in J}$ of elements satisfying the commutation relations $S_jQ=\sigma_j(Q)S_j$, where $\sigma_j$ is a polynomial for all $j\in J$. A concrete representation is given by the operators $Q_x(f)(x)=xf(x)$ and $\alpha_{\sigma_j}(f)(x)=f(\sigma_j(x))$ acting on polynomials or other suitable functions. LÄS MER
4. Descriptive Set Theory and Applications
Sammanfattning : The systematic study of Polish spaces within the scope of Descriptive Set Theory furnishes the working mathematician with powerful techniques and illuminating insights. In this thesis, we start with a concise recapitulation of some classical aspects of Descriptive Set Theory which is followed by a succint review of topological groups, measures and some of their associated algebras. LÄS MER
5. Multivariable Orthogonal Polynomials as Coupling Coefficients for Lie and Quantum Algebra Representations
Sammanfattning : The main topic of the thesis is the connection between representation theory and special functions. We study matrix elements, coupling coefficient, and recoupling coefficients for the simplest Lie and quantum groups. LÄS MER
