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Owner-operators are business owners that began grass-roots efforts to satisfy a need for potential customers i.e. develop a solution for a problem in which customers are willing to pay the owner-operator instead of doing it themselves. The problem and solution may be thought of in terms of a singularity for the customer, however this is not the case. A dichotomy exists where both the owner-operator and the customer have problems and desire solutions based on their individual self-interests. The owner-operators’ problems are manifested in motivations and aspirations and their solutions are displayed as satisfaction. The list of existing motivations and aspirations is too numerable to manage along with the amount of potential solutions. For the pilot study, an attempt was made to categorize the motivations into more manageable groups to ascertain any potential relation with success. The pilot study did not lead to any conclusive results concerning the relationship between motivation and success. However, the pilot study did reveal an associating element between motivation and success i.e. a relation between the problem and solution. That connection was strategy. Strategy was the aid that allowed the gratification to occur. The decision of the owner-operator to choose either a differentiated strategy or cost leadership (low-cost) strategy (Porter, 1980) allowed them to use a more common element where the distinctive nature of the motivations and aspirations was downplayed. The import of this relationship comes into existence depending on how interested various governing and business support bodies are in developing policies whose purpose is to create and/or aid new and existing business ventures (Hamilton, 1987). A continuous review of motivations, aspirations and their relationship with strategy is warranted as older studies become dated, not to history, but due to the fact that economies are in constant flux and as economies change (Hamilton, 1987), so do strategies, motivations, and aspirations. The pilot study focused on success as the resulting construct. During the analysis stage of the pilot study, it was noted that success among various entrepreneurs was difficult to compare and measure across individuals and industries. The result was to shift the construct from success to satisfaction, as it would allow for a simpler definition and better comparisons across entrepreneurs. The question that this dissertation attempts to answer is: What role does motivation and aspiration play in informing entrepreneurial strategy and supporting satisfaction? / Business Administration/Strategic Management

In this work we investigate multi-variable Toeplitz operators and their relationship with KK-theory in order to apply this relationship to define and analyze embedded Toeplitz problems. In particular, we study the embedded Toeplitz problem of the unit disk into the unit ball in C^2. The embedding of Toeplitz problems suggests a way to define Toeplitz operators over singular spaces. / Ph. D.

This thesis contains work from the author's papers Palsson and Sovine (2020); Iosevich, Palsson, and Sovine (2022); and Palsson and Sovine (2022) with coauthors Eyvindur Palsson and Alex Iosevich. These works establish new $L^p$-improving, quasi-Banach, and sparse bounds for several bilinear and multilinear operators that generalize the linear spherical average to the multilinear setting, and maximal variants of these operators, with an emphasis on the triangle averaging operator and the bilinear spherical averaging operator. / Doctor of Philosophy / This thesis establishes new regularity properties for several mathematical operations that generalize the operation of taking the average of a function over a sphere to operations that average the product of several input functions over a surface to produce a single output function. These operations include the triangle averaging operator, the $k$-simplex averaging operators for $k$ an integer greater than 1, and the bilinear spherical averaging operator, as well as maximal operators obtained by allowing the radius of the averaging surface to vary over some range of values.

We develop a technique for identifying unknown coefficients in parabolic partial differential equations. The identification scheme is based on quasilinearization and is applied to both linear and nonlinear equations where the unknown coefficients may be spatially varying. Our investigation includes derivation, convergence, and numerical testing of the quasilinearization based identification scheme / Ph. D.

A (bounded linear) operator J on a Hilbert space is said to be jordan if J = S + N where S = S* and N² = 0. The operator T is subjordan if T is the restriction of a jordan operator to an invariant subspace, and pure subjordan if no nonzero restriction of T to an invariant subspace is jordan. The main operator theoretic result of the paper is that a compact subset of the real line is the spectrum of some pure subjordan operator if and only if it is the closure of its interior. The result depends on understanding when the operator D = θ + d/dx : L²(μ) —> L²(v) is closable. Here θ is an L²(μ) function, μ and v are two finite regular Borel measures with compact support on the real line, and the domain of D is taken to be the polynomials. Approximation questions more general than what is needed for the operator theory result are also discussed. Specifically, an explicit characterization of the closure of the graph of D for a large class of (θ, μ, v) is obtained, and the closure of the graph of D in other topologies is analyzed. More general results concerning spectral synthesis in a certain class of Banach algebras and extensions to the complex domain are also indicated. / Ph. D.

If f is analytic in a neighborhood of ∂D = {z| |z|= 1} and if K = f(∂D), then C-K has only finitely many components; moreover, if U is a bounded simply connected region of the plane, then ∂U = U_j=0<sup>n</sup r_j where each r_j is a rectifiable Jordan curve and r_i ∩ r_j is a finite set whenever i ≠ j. Let μ be a positive regular Borel measure supported on ∂D and let m denote normalized Lebesgue measure on ∂D. If L is a compact set such that ∂L ⊂ K and R(L) is a Dirichlet algebra and if ν = μof⁻¹, then the Lebesgue decomposition of ν|_∂V with respect to harmonic measure for L is ν|_∂V = μ_aof⁻¹|_∂V + μ_sof⁻¹|_∂V where V = intL and μ = μ_a + μ_s is the Lebesgue decomposition of μ with respect to m. Applying Sarason’s process, we obtain P^∞(ν) ≠ L^∞(ν) if, and only if there is a Jordan curve r contained in K such that mof⁻¹|_Γ << μ_aof⁻¹|_Γ. If U is a unitary operator with scalar-valued spectral measure μ then f(U) is non-reductive if and only if there is a Jordan curve r ⊂ K such that mof⁻¹|_Γ << μ_aof⁻¹|_Γ. Let G be a bounded region of the plane and B(H) the algebra of bounded operators in the separable Hilbert space H. If π: H^∞(G)→B(H) is a norm-continuous homomorphism such that π(1) = 1 and π(z) is pure subnormal then π is weak-star, weak-star continuous. Moreover, if S is a pure subnormal contraction, the S^*n→0 sot. / Ph. D.

This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the Hahn-Banach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.