The uses and structures permitted within each zoning district shall be expressly limited to those specified in this chapter. The burden of proof that a proposed use or structure is permitted within a district as specified in this Code shall be on the applicant. No permit or other approval shall be granted if the proposed use or structure does not comply with the provisions of this chapter; provided, however, that amendments to the Official Zoning District Map or text of this Code (including the addition of new zoning district classifications) may be authorized by the Council in accordance with the applicable provisions of this Code.