The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah–Patodi–Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.

The research conducted intends to examine how unexpected changes in employment may affect both exchange rates and interest rates. The results used in the analysis are extracted by running two ordinary least squares regressions with data structured as an unbalanced panel. Furthermore, a two stage least squares regression has been constructed to evaluate how interest rates, instrumented by unexpected outcomes of employment, affect exchange rates through the uncovered interest rate parity condition (UIP). In contradiction to the UIP, relative percentual changes in interest rates had no effect on exchange rates, hence no support could be presented for a causative relationship between unexpected changes in employment and exchange rate movements. In line with previous studies, results are thought to lack significance due to exchange rate movements being measured as the total intraday change, constituting too long of an interval.

Under de senaste 14 åren har den svenska kronan genomgått en period av depreciering mot många andra valutor. Detta väcker frågan om vad som ligger till grund för växelkursens rörelser. Denna studie ämnar därför undersöka om det öppna ränteparitetsvillkoret kan förklara relationen mellan förändringar i växelkurser och räntedifferenser på kort sikt. För att undersöka frågan har två regressionsmodeller konstruerats med räntedifferenser som förklarande variabel och fluktuationer i växelkursen som beroende variabel. Studien begränsas till att undersöka förhållandet mellan Sverige som inhemskt land och Euroområdet samt USA som utländska områden/länder. Eftersom euron och den amerikanska dollarn kategoriseras som “safe haven” valutor inkluderas safe haven teorin som en sekundär aspekt i analysen. Studien använder månadsvis data över perioden 1999-2022. Regressionsmodellernas resultat visar en korrelation som är något avvikande från det öppna ränteparitetsvillkoret. Regressionsmodellerna presenterar icke-signifikanta resultat och studiens slutsats är därmed att undersökningen inte presenterar tillräckligt med bevis för att säkerställa att den sanna relationen mellan räntedifferenser och förändringar i växelkursen skiljer sig signifikant från ränteparitetsvillkoret. / Over the past fourteen years the Swedish krona has undergone a period of depreciation against many other currencies. This raises the question of what factors drive the movements of the exchange rate. This study intends to examine if the open interest parity condition can explain the relationship between fluctuations in the exchange rate and the interest rate differentials in the short term. To examine the subject two regression models have been constructed with the interest rate differentials as the explanatory variable and fluctuations in the exchange rate as the dependent variable. The research is narrowed down to examine the relationship between Sweden as the domestic country and the euro area and USA as foreign areas/countries. As the euro and the american dollar are categorized as “safe haven” currencies the safe haven theory is also included as a secondary aspect of the analysis. The study utilizes monthly data over the period 1999-2022. The results of the regression models show a correlation that deviates somewhat from the open interest parity condition. The regression models present non-significant results and the study's conclusion is thus that the study does not present enough evidence to ensure that the true relationship between interest rate differentials and changes in the exchange rate differs significantly from the interest parity condition.